I wanted to see if your data is coming from a fgdb, mdb, sde or a shapefile? I would then want to know how many layers are you checking out and the "Action" option you are using to check them out of ArcMap. I would then ask if you have had success in checking out one layer at a time, from within ArcMap? These should identify the layer that may be causing the issue being seen, were ArcMap is crashing. Look forward to your responses on this issue with ArcMap and ArcPad. Gracias, Andreas!
How To: Check Out/In data from ArcMap to ArcPad for editing