It is not known whether the appearance of these inconsistencies is an artifact of the approximation, or a real fundamental problem in the theory.
The converse statement, that any QFT which is valid at all distance scales (i.e. isn't an effective field theory) has a UV fixed point is false.
On the other hand, a scenario, where a non-Gaussian (i.e. nontrivial) fixed point is approached in the UV limit, is referred to as asymptotic safety.
[4] Such an asymptotically safe theory is renormalizable in a nonperturbative sense, and due to the fixed point physical quantities are free from divergences.
As yet, a general proof for the existence of the fixed point is still lacking, but there is mounting evidence for this scenario.