This is a task related to this question: Theoretical limit for the number of consecutive checks?.
By a sequence of consecutive check, what we mean is white giving check, black replying with a check, white replying to that with a check and so on. Note that we are talking about a theoretical situation so that 50 move rules or three-fold repetition are irrelevant.
In the linked question, he is asking for the longest sequence of consecutive checks with two conditions:
- Initial position should be legal
- Initial position should not contain promoted pieces.
Suppose we remove the 2nd condition, and relax the 1st one to allow more pieces than legally possible (say, 9+ white queens or 3+ white knights). With these relaxations, is it possible to have an infinite sequence of consecutive checks?
I think the answer to the above question is no (but no complete proof yet).
If such an infinite sequence is there, it should contain a loop for sure. Therefore, the sequence cannot contain pawn movements or captures.
A second question is to construct longest such sequence. Alexey Khanyan's record 54 with conditions 1 and 2 may be surpassable because we relaxed them. (By the way, even with conditions 1 and 2, Khanyan himself thinks that 54 can be improved).
PS: For this question, I am not interested in involving fairy chess pieces or chess variants.