When I try to save a table, I get the error message "Too many fields defined".
Access keeps an internal count of total number of fields in a table and has a limit of 255 fields per table. Each time you modify a field or add a field, this count increases by 1. When you delete a field, Access does NOT reset this counter. So it's possible for you to have less than 255 fields and still get this error message. If your field count is less than 255, just compact the database again which should reset the internal field count counter.