There is no "Catch 22", just a false dilemma.
The underlying assumption is that either the species will die out in a relatively short time (no more than a few centuries) or it will be so well adapted that no evolutionary change is likely.
However this is not the case.
Even in a highly stable environment the fitness could be arbitrarily close to 1 . If it was a very little below 1 then the population would only decline very slowly, giving time for speciation.
But real environments often include short term variations like bad weather. A species that would otherwise hang on can be wiped out by a run of bad luck. If that required conditions that were expected to happen once in 2,000 years then on average the species wuld last 1,000 years - long enough to evolve into a new species which could better survive.
And we are not restricted to short-term variations. Environments can change over time. If the change is slow enough then a species which would otherwise die out can evolve to "track" the change. Examples include so-called "arms races" where predator and prey each drive the evolution of the other. As the predator improves it's ability to catch the prey, the prey is driven to evolve ways of better evading capture - and vice-versa.