How to help a student researcher with narcolepsy continue research
I have had Narcolepsy for ten years now. I am also currently an undergraduate at university. In my opinion, based on personal experience as a person with narcolepsy, there are a few things important to consider.
Firstly, the severity of narcolepsy is different for all those who suffer it so abilities vary. I am at university full time and whilst I am offered accommodations to assist me, on the whole, I produce high quality work.
Secondly, a person with narcolepsy may doubt themselves regardless of their abilities because others around them are quick to doubt them. This is why, on most occasions, I have not disclosed my condition to employees. Once I am employed, the quality of my work speaks for itself and then I disclose it for safety reasons. This is an internal battle because I fear that I am being untruthful to start with. At the same time, I know the stigma narcolepsy brings and that given the choice between a candidate with narcolepsy and one without, I would lose. If this person has told you about their narcolepsy it means they trust you and respect you and feel compelled to be completely truthful with you. They probably don't want to let you down so they will probably downplay their abilities in fear of this.
Whilst narcolepsy is characterised by 'sudden uncontrollable bouts of sleepiness', it's usually brief and full alertness is resumed after a short nap. Narcolepsy occurs because the hypocretin/orexin have been fought off by an autoimmune disease. This means sleep/wake cycles aren't regular. A person with their hypocretin intact do all their sleeping in one block, usually when the sun goes down. A person with narcolepsy sleeps in smaller blocks of time and stays alert for a shorter amount of time. Theoretically then, a person with narcolepsy can be awake and alert for the same number of hours a day as a non-narcoleptic but needs to do this by by breaking it up into smaller blocks. (You could liken this to differences in diet - some people eat three big meals a day while some people eat six smaller meals a day.)
To conclude, yes narcolepsy makes my life more difficult. I wouldn't be able to succeed at university without the support and understanding I get from the staff. But life is full of challenges and it is the way in which we deal with them that sets us apart. If you have developed a good working relationship with this person, then they already fulfil one important aspect of those needed for the position. A person with narcolepsy is aware of their shortfalls and given the chance, will do what is needed to overcome them. Don't let a diagnosis change your perception - just because a person doesn't have a medical label attached to them, doesn't mean they don't have other relevant faults or issues.
My advice is to write down what is required to fulfil the needs of the research - do it in measurable terms. For example., how many hours a day/week is sufficient? Then sit down with this person and discuss it with them. Approach the requirements as you would anyone else. (For eg. Can you commit to these requirements? etc) If you were happy with their work previously tell them that. Also admit that you don't know much about narcolepsy but you know that everyone is different. Tell them you want them to succeed and you have faith in them. Tell them how important the work is to you and if you think you are a good team, say so.
I hope this has been helpful and thank you for not listening to your human resource department who clearly lack knowledge and empathy.
As a doctoral student (and research assistant) with narcolepsy I will echo much of Stacey's answer. After outlining the responsibilities and expectations of the job, I recommend meeting with the student to discuss possible accommodations which may allow them to conduct research without creating undue burden on your lab and project. As you mentioned, a flexible work schedule that accommodates their sleep schedule is one option.
Personally, I've worked with my mentor (the PI) to create a very flexible work schedule and we focus more on the outcome of my work than the hours I spend working on it. There are rare times when (due to health insurance glitches) I can be without my medication for a few days up to 1 week. When this happens I make my mentor aware of how this is impacting my functioning; at times we've had to re-prioritize projects during those "med gaps" because I am unable to work as intensely as I normally would. Similarly, because narcolepsy medication can include stimulants, if I catch the flu my physician advises I skip my narcolepsy medication in order to allow my body to naturally rest. So, my mentor is also aware that if I catch the same flu bug as everyone else in the winter, it might knock me out of commission for a few days. Once I am back on my feet (or have received my meds from the insurance company) I make up the hours I missed in the following week.
As mentioned in the other answers, narcolepsy has a range of severity and so the accommodations needed will vary as well; you will have to decide what works for your lab. One last note: as a graduate student there is often an emphasis on working excessive hours or going without sleep to meet the demands of research, classes, etc. This is not an option for me and at times my work output has been compared to classmates who sleep 5-6 hours a night to "crunch" large projects. I think sometimes with "invisible" disabilities or illnesses it is easy to forget the subtle or significant ways it can impact that person's life. The fact that you are seeking information on this topic and investigating ways to be supportive of your student is great.
This may be no direct help, but I knew a narcoleptic in high-school. This is a serious condition. Because of the main symptom, excessive daytime sleepiness, it is very hard for affected individuals to remain alert and direct their focus to tasks such is studying. reading, etc. For comparison, wikipedia says, that narcoleptics feel during the day "comparable to how non-narcoleptics feel after 24 to 48 hours of sleep deprivation" (try to imagine how it would feel like to perform under those circumstances). This is obviously a great hindrance to people in general, but perhaps even more so for academics.
Furthermore, it is very important that affected individuals manage somehow to cope with the condition (which is very hard, serious lifestyle changes/adaptions are necessary), as an excessive use of stimulants may worsen the condition over time. I find this an important point, since people in academia are known to be subjects to stress, depression, feelings of being overwhelmed, imposter syndrome, etc, which all could push the student in question to increasingly use the therapeutic stimulants.
So, in my opinion, if the individual is responsible and has a relatively stable personality, I see no problem in supporting them in their endeavor, by trying to (reasonably) adjust their working environment to their needs.
I'm a strong proponent to inclusion of disabled individuals, so I suggest you should let the student finish the said project, so they might get a feel themselves, if that is really their future. A career in academia isn't for everyone, so there is no shame in quitting and moving on, regardless of any medical condition.