Why do I have to keep resetting my Apple ID password on my iPad?

I just got a new iPad Air recently, and I'll be real honest, I'm just not experienced at all the new little electronic gadgets (guess what, I'm old, what a surprise, get over it, stop laughing), so it's been a lot of trial and error getting this thing set up, but the thing I've been having the worst time with is my Apple ID password. I've used the same one for years on my Mac Pro with never a problem, but for some reason, for this iPad I had to change it. Then after I changed it, it worked fine on the iPad for a while, but then the next day when I try to log in again, it tells me I'm entering the wrong password. So I've changed it a few times in the last few days, and it'll work fine for a while, until the next day. What gives? Is there something I'm just not "syncing" right or what? This is really one hassle I'd like to be done with. Any help anyone can give will be very gratefully appreciated.