How hard is it to re-enter academia as a postdoc in mathematics?

The possibility of getting a postdoc starts to drop rapidly as you become farther away from your PhD, regardless of what you are doing in the meantime. This goes double (or triple) if some of that time is spent without having publications.

What is your end goal? Certainly not to hop from postdoc to postdoc for the rest of your life. Answering this question will probably help you decide what to do. Take another postdoc if you are hoping to become a professor or academic researcher. Take a software development position if you are wanting to leave academia. Don't hold on to too much hope of being able to go back to academia in pure math after leaving for more than a year.

I think this would be effectively impossible with n>1. Many postdoc positions in math have a formal requirement that applicants have completed their PhDs within the last k years, with k usually equal to 3 or 4. Even when this is not a formal condition, the culture in math postdoc hiring makes it very unlikely that you will be seen as a competitive candidate for another postdoc after 2 or more years away from academia, unless perhaps your record is so strong already that you can be considered seriously for tenure track positions even now (in which case you should apply for those positions and not postdoc positions anyway).

With n=1 I think you may have a realistic chance, especially if you can offer a convincing explanation of what you were trying to achieve with the software development “gap year”, and especially if you take care to maintain visibility in your research community during your year in industry by continuing to publish and/or going to conferences.

Disclaimer: the above represents my opinion only and I cannot vouch for its accuracy. You should seek opinions from multiple sources before reaching a decision, including trustworthy senior people who are more familiar with your personal situation and goals. Anyway, good luck!