...Anyway, I cleaned the gas cap gasket and mating surfaces. Drove the car a few days (about 10 restarts) but the light is still on.

Well today I took the car for two 20 minute highway rides. Low and behold, on the way home I glanced down and the that little Engine light was not staring back at me.
Let's hope it stays that way.

 

It may have been transient (loose cap), it may come back on. The EVAP tests don't run continuously.

Evaporative Emission System Leak Detection with Purge Monitor

This monitor requires a cool down cycle, usually an overnight soak for at least 8 hours without the engine running.

The ambient temperature must decrease overnight - parking the vehicle outside is advised. To run this test the fuel level must be between 15-85% full. For the monitor run conditions select the EVAP MON PRE-TEST in the scan tool, OBD II Monitors Menu. The Purge monitor will run if the small leak test reports a pass. Criteria for EVAP monitor:
Ç Engine off time greater than @ one hour.
Ç Fuel Level between 15% and 85 %.
Ç Start Up ECT and IAT within 10° C (18° F).
Ç Vehicle started and run until Purge Monitor reports a result.
NOTE: If the vehicle does not report a result and the conditions where correct. It may take up to two weeks to fail the small leak monitor. DO NOT use this test to attempt to determine a fault. Use the appropriate service information procedure for finding a small leak. If there are no faults and the conditions are correct this test will run and report a pass. Note the Small leak test can find leaks less than 10 thousands of an inch. If a small leak is present it takes approximately one week of normal driving to report a failure.

I had this light coming on continuously for months (I kept clearing it and it kept returning). It finally became P0455 (large leak) so I went and bought a $12 gas cap to see what happened, and it hasn't come back on for over a month.

For the record, I only got the "gascap" message one time over 6+ months, but it seems the gas cap was indeed the problem.

 

Well this is a coincident reply after 5 months because ...
All was well, then about 2 weeks ago my GASCAP light came on. This was the day after I got gas. So I pulled over and removed then re-tightened the cap. After a few miles of driving the GASCAP light went off. It never gave me the check engine P0456 code.
The cap doesn't feel as tight as it should. The gasket is probably worn a bit and with contraction in the colder weather I expect I'm gonna get that GASCAP message again. Time for a new cap.

tinbgith: What cap did you buy? from dealer or aftermarket?

 

I got an aftermarket cap from O'Reilly:
http://www.oreillyauto.com/site/c/d...e=Dodge&model=Caliber&vi=1443610&ck=Search_gas+cap_1443610_4012&keyword=gas+cap

I drilled a hole (1/4") into the cap to keep the factory tether. The tether is hard rubber, and was easy to pull out of the original cap and push back into the new one.