These devices are just a bother... I get similar FOB's sometimes in my shop, A considerable amount of problems are caused by bad batteries, or bad battery contacts. You need to get the procedure to "Re-program" your units. Usually, it is a simple job, and I am sure you would be up to the task. Also Often, depending on exact type, the Antenna connection, can be "dinky" and need attention. Usually, a "Reset" remove battery and reprogram, sorts the problems out. However sometimes you get one that faults all the time, this is caused by damaged RAM onboard the IC, that "Runs" the FOB, Also often they get fractures in the solder joins, on the actual PCB, Often may problems are permanently sorted by a quick going over of suspect looking joints, with a Hot soldering iron. I have given you some handy links below. Also a manual for your vehicle.
http://en.wikipedia.org/wiki/Remote_keyless_system
http://www.keylessride.com/
http://www.ehow.com/way_5344037_troubleshooting-remote-keyless-entry.html
http://www.ehow.com/how_6194237_program-keyless-entry-remote-fob.html
Above how to program Dodge keyless entry, may be of help.
http://carpdf.net/2005-dodge-grand-caravan-owner-manual.htm
Above is a manual, inside there are programming instructions too.