Take a look at the following article which describes a similar problem:
ACC: Error Message: Can't Open Any More Tables
http://support.microsoft.com/default.aspx?scid=kb;en-us;165272
This generally happens when you either have too many forms and reports open
simultaneously or you have a few complex forms open.
Also keep in mind that if your database is split (which is typical for a
multiuser database), each time you open a table you are actually using two
table ids. On a complex form with a couple of subforms with combos and
listboxes in the main form and in the subform(s) you can exhaust many
tableids very quickly.
There are ways to improve the overhead of a form. Typically you would start
by unbinding subforms which are on hidden pages of a tab control then using
the Change event of the tab control to bind/unbind each subform control as
its page is shown or hidden.