In ArcPad 10, extra support was added to the TIFF module to support TIFF images that comes from ArcGIS. If you have a problematic TIFF image, I would very much like to get a copy of it so I can analyze it.
Otherwise, can I recommend that you use ArcMap to generate better TIFF images for ArcPad using the following steps:
1. Load your original image in ArcMap
2. In the Table of Contents, right click on the image, and select Data > Export Data
3. An Export Raster Data dialog should appear
4. Set Format: TIFF
5. Check Use Renderer (* important *)
6. Check Force RGB (* important *)
7. Click Save button
This should produce a TIFF image that will load in ArcPad.