There were two previous posts for this question back in Dec 2002 with no resolution.
This problem exists when using a MEMO field (also tested with OLE Object field and get the same error). The senario is that data is entered into this MEMO field. Later the field is edited and more data added. This continues to work until the field has around 2k worth of characters at which time an attempt is made to save the record and then the error message "Could't Update; Currently Locked by Another Session on this Machine" appears.
One work around seems to be to add another record and then come back to this record and then you can get past the 2k limit. But then the extra record needs to be deleted.