An app cannot install itself. So if it's reappearing there are really only 3 possibilities:
1) Someone has your Google password and keeps pushing the app back. This case doesn't sound like that to me.
2) Another app that's still installed on your phone is reinstalling it (either one you installed or, one some particularly dodgy phones, one the manufacturer installed).
3) It's actually in the system and you aren't really uninstalling it (I've met cases where the system tells you it's uninstalled but it isn't, though it's usually on the next restart that it reveals itself to still be present).
One way to test whether it's one of the apps you installed: boot into safe mode, uninstall it, then stay in safe mode and see whether it returns. No user-installed apps run in safe mode, so if this prevents it returning then it is one of the apps you installed that's responsible.
Another, nastier, possibility is that a pre-installed app is responsible, possibly gaining this malicious behaviour after an update. The classic case of this was "peel smart remote", an IR blaster app that some manufacturers pre-installed, where the company added an advert-filled extra lockscreen to the app which was then pushed to people who'd never chosen to install it or ever used it as an update. If it's something like that then disabling the culprit will stop it.