Hi veljanovski,
I have carried out this reaction on a small scale with 7M methanolic ammonia, at room temperature and without using any pressure device. It IS very slow (days), but it works, as March or other OrgChem books say. I've also used other amines, as MeNH2 and EtNH2, even in water/MeOH, without observing any hydrolysis of the methyl ester.
You may need to use an excess of amine - if you can, of course - to speed up the process.
If you can't, a good way round could be hydrolysing the methyl ester with, say, NaOH in water/THF and then couple the free acid and the amine with any coupling reagent you like.
For the rest:
1. the equilibrium constant is favourable, i.e. the amide is more stable than the ester; just look at the very harsh conditions needed to hydrolyse an amide...; and to my knowledge you can't do this with an alcohol.
2. I guess an acidic catalyst is not likely to help, especially if you use aliphatic amines, because they will just mop up the acid, making it unavailable to protonate the ester (besides, I think a different mechanism operates here)
3. I don't really understand how you analyse your reaction mixture. You say you use NMR and don't see MeOH; but do you see the ester methyl group or not? And what about the residue coming from your amine? Do you see it in the product or not? I would advise you to spend some time evaluating how good your analytical methods are before you state that a reaction doesn't work.