When you program the T2 you must have a freshly charged battery. When you learn from other remotes you must ahve fresh batteries in them as well. Do not use batteries supplied with new equipment. Throw them away and use Duracell Ultras. Remove the batteries after learning the codes to the T2.

You may have to remove all the commands from the T2 that you are having problems with and then reloading them after you "re-learn" the IR command from the donor remote.

I had all the problems you described and this process corrected it.