Conjecture on infinitely many nonterminating cases of the heuristic palindrome algorithm

For a natural number $N$, consider the heuristic algorithm used to search for palindromic numbers $A$ and $B$ satisfying $N=A/B$. Nontermination conjecture. There are infinitely many natural numbers $N$ for which this heuristic algorithm fails to terminate.

The source gives explicit examples where the heuristic fails to determine a solution, while a guaranteed decision algorithm resolves the cases; it does not establish whether infinitely many nonterminating instances exist.