I would keep it. I understand your feelings. I'm a mechanically inclined person and just accepted the fact that I would have to do all of my own repairs and maintenance regardless of any warranty. The nearest GM dealer I would even let touch my truck(s) is 90 miles away.
I bought my H3T in 2009 brand new. Great service from the dealer (90 miles away). I bought a 2008 H3 Alpha in Jan. 2012. Traded it for a 2004 H2 in Dec. 2012. Got all nervous about fuel economy, lack of parts, parts costs, service cost, age of the vehicle, etc and traded it in on a brand new 2013 Scion tC in May. Thought life would be great. Good MPG, warranty, free service for 2 years. Worse mistake I ever made in my life. I hated that car more every day I drove it. Plus, the dealer ended up being worthless (toyota/scion of Scranton, PA if you are curious). Took a bath on it and traded it in on (or more like against) a 2014 Jeep (! a JEEP!) Grand Cherokee Overland for the wife 2 weeks ago. I shopped around and the Jeep place actually gave me a very fair value for the car. I could've burned $6,000, kept the H2, and still would have been ahead.
I just got a Base, Base, Base model '07 H3 Saturday. I actually enjoy driving it more than I did the Alpha. The 3.7 with a 5-speed is so much nicer than the auto.
Get familiar with the issues the H3 has. Either accept them and keep the H3 or if you can't get over them - buy something else. Think long and hard about it. If you make the decision in anger, you will regret it.
I'm keeping the two I have now for a long time. I'll be building molds/dies and casting/stamping parts for the H3 someday if I have to. The '07 is going to be my toy. I'll be doing some heavy mods to it soon. It's my fourth HUMMER and I've loved them all.
I'm starting the Eastern Division of the HUMMER Rescue Foundation No Kill Refuge. Any unwanted HUMMER's may be dropped off 24/7 without question. I will even come to pick them up.