I have exactly the same issue. Have to remove and add my 310XT everytime I want to upload an activity (which goes, as it finally works, very, very slowwwwwww.)
Try clearing out all the activities on the Forerunner 310XT that have already been sent to Garmin Connect. Or at least anything older than the last 30 days if already uploaded. Then move the pending Sync folder on your computer to the Desktop and restart Garmin Express. There could be old files in the Sync folder slowing the sync down. Here are the instructions to do so:
Press the Windows + R key together
Type %ProgramData% in the box
Click OK
Double click Garmin
Double click CoreService
Double click Devices
Double click the folder with the 10 digit Unit ID for your device (can be found in the About screen on the device if there are multiple folders present)
Right click on the Sync folder
Left click on Cut
Minimize the Windows Explorer/File Explorer window
Right click on the Desktop
Left click Paste
Close Garmin Express
Right click on the Garmin Express icon in the System Tray
Left click Quit
Click Quit on the prompt to run in the background
Once done, launch Garmin Express and try the sync again. The Sync folder will be recreated. This folder should be empty after a successful sync. If you are still having issues, contact Product Support by phone for further assistance.