Microsoft Windows95 Dial Up Networking (DUN) sometimes will not offer an option to remember the password. FishNet has researched this further on the Microsoft Knowledge Base, and the two articles below in particular seem to address this issue.

Dial-Up Networking Password Is Not Saved

Save Password Check Box Is Unavailable

Some of the actions that they recommend may be hazardous to your machine's health, so be careful. In particular if part of the fix is to edit the registry, be very careful to make a backup copy of the registry before modifying it.

You may wish to check out FishNet's Windows95 DUN setup instructions also, specifically the section on Dial Up Networking Configuration. This will help you configure DUN if you need to change it in any way. FishNet used to recommend that the Client For Microsoft Networks not be installed in the default Network configuration, but the articles above indicate that can be a cause for not being able to save the password.