From this answer, it sounds like Pokémon are able to call for help an unlimited number of times. In addition, it looks like there are some Pokémon that can only be encountered when they respond to other Pokémon's cries for help.
How can I effectively chain an encounter to get Pokémon like Pikachu or Mareanie?
Best Answer
From the same Serebii link as above, there are a few strategies to improve your chance of having a Pokémon call for help:
Due to Adrenaline Orbs being usable only once per battle, as noted by @UnknownZombie in the comments, using additional Adrenaline Orbs is a very effective way to pass turns during battles where you are trying to chain SOS Pokémon, as you will not be able to use another Adrenaline Orb, but it will use up your turn.
A third way to improve your chaining probability is to use a Pokémon with the ability Intimidate, Unnerve, or Pressure.
Thus, the three main strategies are to keep the Pokémon at low health, to use an Adrenaline Orb, and to use a Pokémon with Intimidate, Pressure, or Unnerve.
As an aside: