A family of Microsoft relational database management systems designed for ease of use.
No, I use the 32bit version and have most of the symptoms described above, including yours.
Mine does not run out of databases immediately, though. It takes a while with lots of SQL queries going to a linked ODBC database before it starts to complain.
Another issue I get often is an error when I close down Access. The error states that:
You attempted to open a database that is already open by user 'Admin' on machine 'nnn'.