You may simply be looking at a worn-out power button. iFixIt has a repair guide all about fixing this exact issue. Take a look-see at this [guide|25403] repair guide for the how-to. Or, if it's an '''HP Slate 7 Plus''', it may be a bit tougher to fix however, here's a post about a possibly similar issue: [post|300575].
If those links do not help, please provide more detail about your particular power button issue. For instance...
* Can you get it to work sometimes but not others?
* When the screen turns on after rebooting the tablet, can you tell how much battery is left?
* Does the power button seem loose and/or can you wiggle the button more-so than normal?
Good luck,
_rs