How many times can Pokémon call for help?
There is no limit to how many times a Pokémon can call for any ally. For example, one user on Reddit chained 100 Rockruff calls for an ally to get a shiny Rockruff.
The reason why calls for ally are unlimited is because it is the new method of chaining Pokémon to obtain Pokémon with increased chances of being shiny, having better IVs, or potentially having their Hidden Abilities.