Hi 1976kjell,
Welcome to Vista Forums!
Let's make sure Hotmail is set to save the password and logon information. Go to Start / Control Panel / Mail / Setup Email Account and Directories and double-click on your Hotmail account. Confirm that the box to remember the password is checked.
If it's set right there, I recommend you change the password for Hotmail and this may trigger auto-complete to save the new one and you'll be good to go. If not, you may at some point have told Hotmail not to save your password (which could be over-riding autocomplete) or responded that way to auto-complete and so now it is set to no longer ask. If the latter is the case, the only solution is to reset auto-complete (where you will lose all current auto-complete items) and re-start from scratch - beginning with Hotmail to be sure it works this time.
Whether you want it enough to reset auto-complete (assuming that even works - there's no guarantee that will solve the problem. I don't have that problem with Vista and Hotmail, but I'm not certain where the information is coming from - it may not be from auto-complete or may be being blocked some other way we haven't yet figured out) is entirely your risk and your decision.
I hope this helps. If you don't want to delete auto-complete but want to pursue Hotmail password blocks further, post back and I'll try to research it further though it may take some time.
Good luck!