I posted this same issue in the Garmin Edge 305 forum. Got on reply saying that the 305 has a problem with spurious stop/starts due to an overly sensitive stop/start button. Perhaps, but it seems it would have happened more often. I've researched the 305 and I never heard of this problem reported.

I went to the Garmin site and contacted Support via email. Got the following reply. I'll give it a try tomorrow.

Please do a master reset on your Edge. Doing a master reset will delete
all user data, but will also delete any corrupt system information that
may be causing the issue. To do a master reset, with the unit off,
press 'mode' + 'power' for a few seconds. You'll be asked if you're
sure you want to delete all user data, select yes.

I would then advice you to reinstall the software or “firmware” on your
unit.

01. Please go to the WebUpdater webpage by clicking on the following
link: http://www8.garmin.com/support/colle...t=999-99999-27

02. Select the Download link next to your Operating System.
03. Agree to the Terms and Conditions.
04. You will see a link labeled Download, please click on it.
05. You will be asked if you want to Run or Save the file, please click
Run. (If there is no Run option please select save. When your file is
finished downloading, please Run the program.)
06. After the file downloads, you may receive a security warning when
you attempt to run the software; if you do, please click Run / Ok.
07. Software will unpack itself and new window will appear; please click
Next.
08. A license agreement will appear; please agree to the terms and then
click Next.
09. The software may appear to freeze for a moment during installation,
this is normal. (Installation should take less than 10 minutes.)
10. After the installation, please click Done.
11. The WebUpdater program will launch - again, please ensure that your
unit is connected to the computer and turned on.
12. Click Next; you should then see your device listed (if you do not,
then please click on Find Device). Once your device is listed, please
click Next.
13. A new window will appear with information about the update for your
unit, please click Next.
14. A new license agreement or summary of the update may appear, please
click that you agree and/or then click Next.
15. The unit's internal operating system/software (sometimes called
"firmware") will then be updated.
16. Once the download is complete, please click Finish.
17. You may now disconnect the unit; it is ready to use.

If these steps do not correct the issue, please let us know.