I have had some success minimizing ArcPad on Windows Mobile units by simply tapping the Start or Windows icon above ArcPad window; I am also able to minimize ArcPad and go to main screen by pushing the Windows button. On Windows Mobile OS units, you can only switch to another application via the Today screen or through the use of third-party application switchers; some users have told me they use WkTASK but please search the Internet as Esri doesn't recommend or endorse any of these applications and other users are your best resource.
This is a great topic for ArcGIS Ideas site and I encourage you to submit it under ArcPad product.
