Sometimes when you try to run the Handheld Contact installer it will try to overwrite the existing application but it cannot.  Below are steps to follow to correct this:

1. Open the Task Manager and stop the current installer process.
2. Go to: C:\Program Files(x86)\Handheld Contact\HHC Enterprise Edition.  Note: If using v4.2.10.0 or lower, the install location is found here: C:\Program Files(x86)\Keystroke\HHC Enterprise Edition
3. Look for two files called 'settings.hhc' and 'HHCSYNCLOG.FDB'.  Copy them to a common location such as the Desktop.  They will be used again.
4. Once the files are moved, go to the Add/Remove Programs features within the Control Panel and manually remove Handheld Contact.
5. When it is finished, run the new installer again.  If you need to download it again, you can obtain it from: http://www.handheldcontact.com/downloads.php.
6. Install HHC again as if it was a new program.  When completed, press the Finish button.  Handheld Contact will try to open automatically.
7. Cancel the set up once opened.
8. Take the two files that were copied from above and replace it back within the directory from Step 2.
9. Overwrite the existing settings files that were created from the new install.
10. Go to the Desktop and launch Handheld Contact again

UPDATE: Another (quicker) solution is to stop the current sync.  The reason the app upgrade is stalling is because the HHC Service is currently trying to sync.  Here are the steps to get the upgrade to work properly again:

1. Ensure Handheld Contact is closed.
2. Cancel/Stop the upgrade from the Task Manager.
3. You can click here to restart the HHC Service. 
4. Once that is restarted, go back to the Downloads page (as seen above) to download/run the installer again.