You might think the form is trying to connect to the same database location from the other computer when it really isn't.
When creating the Main Connection to the database file, don't use the Browse button to locate the database on the network - the resulting path may include drive letters/mapped drives that are specific to the computer you are designing the form on, instead manually type in the URN path to the database. This is usually something like //computerName/shareName/folderName/folderName/databaseFile.mdb
Using the Browse button will automatically change the path to the database to using any mapped drive letters you have set up on the designing computer.
It's just one possible cause - but one I know I was caught with a few times.