There is no fixed number of attempts for GPSC exams; eligibility depends on age, not on how many times you've applied.
As long as you are within the eligible age limit, you can appear for GPSC exams regardless of the number of prior attempts.
A general category candidate (max age 35) may get about 3–4 realistic attempts, depending on notification frequency.
SC, ST, SEBC, and female candidates have higher age limits, which naturally give them more attempt opportunities.
Physically disabled candidates benefit from 10-year age relaxation, increasing total possible attempts significantly.
GPSC officially does not cap the number of attempts in any of its recent notifications — only age criteria is enforced.