Are you using a fitted case with your iPad?
If you are using a case, try removing (or at least re-fitting) the case. Some cases can mechanically interfere with the iPad's physical volume buttons.
Similarly, buttons have been known mechanically fail or internally collapse - losing their "click". If the any of the physical buttons have failed, the iPad must be repaired. It is a common misconception that an iPad (or iPhone) can remain fully functional with damaged or defective physical buttons.
Whilst Accessibility features (such as assistive touch) can be used to augment the User Interface, these features cannot be used as a substitute for physical button sequences that must be used to trigger system recovery actions. If a physical button has failed, sooner or later you will encounter a situation from which you cannot recover.
If required, you can arrange repair of your iPad either by (a) visiting the Genius Bar at your local Apple Store or Apple Authorised Service Provider (AASP) - or (b) using Apple's mail-in repair service:
Genius Bar Reservation and Apple Support Options - Apple
iPad Repair & Service - Apple Support