Why can I sometimes not enter my password on my iPad?
Just like a computer, an iPad is a software-driven device, and unresponsiveness like this is commonly the result of imperfect memory management.

From my experience, the leading cause of iOS software instability is running low on application memory. This can happen after long periods of use without ever power cycling the device — days or even weeks. (How often are you needing to power cycle your device?) Even if the device works great, if it has been a while, turning it off and on is a healthy action, as it can re-allocate its full memory once again, just like restarting a computer.

If you aren’t noticing delayed or unresponsive behavior elsewhere, then perhaps a backup and restore would be a good thing to try, to rule out corrupt or damaged system software.