Are there any DIY remedies for a iPhone 4 home button that doesn't always register? The home button on my iPhone seems to work on and off. 

It does take me back to the home screen but it feels like there is a loose connection and does not trigger on every press.

Is there a fix to this besides Apple support?
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.