Is the Safari tool bar a dark grey instead of the usual white with black and blue icons?
If so, you've accidentally put Safari in Privacy mode, and it will not remember history, cookies, or other information (like log in credentials).
To leave Private mode, tap the double square icon at the top right of the screen, then tap the Privacy button (also top right) so that it is no longer highlighted. Safari should return to it's white tool bar and remember your log-in credentials when appropriate.
The other possibility is that Safari's Block Cookies settings have been changed. Go into Settings > Safari and find the Block Cookies settings (near the bottom). The best combination of security and usability is to have this set to Allow from Current Website Only.