We reconsider the problem of the critical behavior of a three-dimensional $O(m)$ symmetric magnetic system in the presence of random anisotropy disorder with a generic trimodal random axis distribution. By introducing $n$ replicas to average over disorder it can be coarse-grained to a $phi^{4}$-theory with $m times n$ component order parameter and five coupling constants taken in the limit of $n to 0$. Using a field theory approach we renormalize the model to two-loop order and calculate the $beta$-functions within the $varepsilon$ expansion and directly in three dimensions. We analyze the corresponding renormalization group flows with the help of the Pade-Borel resummation technique. We show that there is no stable fixed point accessible from physical initial conditions whose existence was argued in the previous studies. This may indicate an absence of a long-range ordered phase in the presence of random anisotropy disorder with a generic random axis distribution.
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