^ Indeed. Possibly as time goes on it actually gets harder rather than easier, as the regenerative process gradually "eats away" at the individual. They can be 'renewed', but it causes a little decay each time and it only gets harder and harder to cope with it. Possibly the 13 lives 'limit' is simply a consequence of this. 12 regenerations is all a Gallifreyan body can actually muster before it just breaks down naturally.
The Master is a case in point; we see on screen that he can
in fact regenerate beyond his 13th incarnation, but to do so caused his 14th body to immediately decay and fall apart. Only by transfering his living consciousness to other bodies (something which was in itself of only variable success) was he able to survive.