Apple - Are there any DIY remedies for a iPhone 4 home button that doesn't always register?

You could take it apart and fix it yourself, however it will void any warranty on the phone. You can view the iFixIt Repair Guide for steps for removing and replacing the Home button. Note that you will have to take apart the majority of the phone to get to the button.

Your best bet would be to go to Apple for a repair or find an authorized repair service shop to do it for you.

Thanks guys!

Btw my phone is out of the warranty period, so no luck there.

Here is something I found in the forum that can help as well (not as much as a fix than a workaround) - AssistiveTouch, which is baked into iOS. It provides an overlay on the screen for several functions, including the Home button. Credit goes to Bentsai's answer.

Works great!

There is a trick I've used many times to 'fix' my home button, it only takes a couple of seconds and it works every time. [But, disclaimer, the issues you have may be something different.]

The solution is to insert a charging cable into your iPhone (it doesn't need to connected at the other end, just the bit that goes into the iPhone). Then if you put your finger on the botton of the connector (the solid bit that goes into the iPhone) and pull it towards you.

It would appear that the hardware parts are somehow separating inside the iPhone through repeating use of dock stations / connectors, and this just helps to squeeze the parts back together - albeit it isn't as good as it worked on day 1.