You cry.
The link will not break. It just can't. As long as you have a geodatabase in the same location that you checked out, all is good. You can even delete the GDB and put a new one in its place and it has worked for me.
Now, if you were to change the location of the GDB, you might be able to go into the .axf and change the checkin GDB, but I haven't tried it. The .axf is just a SQL compact file. You can go into ArcPad Studio and snoop around all of the tables and find the connection string to the GDB. That might work, but I'm not sure.
If all else fails, you can just export the data as a shape file and import it into your GDB.