I can't speak to your Tmax failure, but dilution is generally done to make the development time tractable (as mentioned above), or to change the behaviour of the developer in some important way.
Originally Posted by ezwriter
For example, D76 contains a silver solvent which becomes rapidly less effective with higher dilutions. So D76 stock gives very smooth negatives at the cost of some resolution because the grain has been heavily dissolved; D76 1+1 is a nice general-purpose intermediate and D76 1+3 gives very sharp negatives with practically no solvent effect.
Rodinal also changes with dilution: at around 1+25 to 1+50 it acts as a normal developer with no solvent. At 1+100 or more and longer times with no agitation, you get local exhaustion of developer in the highlights, so it becomes both compensating and sharpening.
I don't use Tmax dev so I can't tell you what it will do with varying dilution.