Hi Jim - Sounds frustrating. I too am a user of many years, yet to find an alternative that meets my needs as well as Approach has :-(
Not knowing what you've tried - or your level of expertise - but have you tried ruling out possible (obvious?) causes - e.g. that the .apr view file is in fact attached to a different .dbf than you think it is (assuming you are using the default) data file ? You could try opening the .dbf file concerned directly (select file type to open DBase IV and it will display those )and writing data to that file direct. Ensure it works there. Obviously be careful not to simply do a "save" over any .APR file by the same name - which Approach will prompt you to do. You could also try creating a simple/basic .apr file that way and see if data edits are saved.
Secondly, I assume you are using data that is stored and accessed locally on your own hard drive (so we can rule out any Internet read/write protocols and issues ?
Thirdly, (on a similar note to 2) I guess it's worth revisiting exactly how Approach 'writes' data changes to the data file. What I do know from experience is that, despite what one has supposedly 'entered' in say an .APR form, if one presses "escape" any changes that may have seemed 'entered' changes are lost. Which indicates that is that changes data is not actually 'written' (to the disk) until one has tabbed or moved on to another record and/or 'forced' a data 'save' e.g. by used the carriage return looking Smarticon.
Anyway, just some ideas from a non-expert. Hope it helps, but either way - best of luck. Tim