I haven't had the missing search field problem for some time. Back when I first got my iPad, in iOS 6 days, I knew little about how best to use the iPad. I remember that after having iReal b, as it was called in those days, open for a long time, the search field for songs would disappear without warning. At some point, I learned about closing apps that were misbehaving. Closing iReal b solved the problem and restored the missing search field. Nowadays, I regularly close all of my apps before going to bed at night, and do an occasional restart if my iPad seems to misbehave. This kind of regular maintenance sees to prevent problems that seem to occur when too many apps are open. My wife, who enjoys watching videos and TV programs on her iPad often has problems when too many of these apps are open and sometimes the only way to fix her iPad is to do a restart.
From what I have read (and don't take me as an authority), doing a restart is a fairly harmless procedure. Doing a reset is a more serious action and should only be performed if doing a restart does not fix a problem. In the iPad User Guide for iOS 8.1 from Apple: "If something isn't working right, try restarting iPad, forcing an app to quit, or resetting iPad."
That's about all I can tell you about the missing search field problem.