The regex would be:
/\(.\{-}\zsPATTERN\)\{3}
So if, for example, you want to change the 3rd 'foo' to 'bar' on the following line:
lorem ifoopsum foo lor foor ipsum foo dolor foo
^1 ^2 ^3 ^4 ^5
run:
s/\(.\{-}\zsfoo\)\{3}/bar/
to get:
lorem ifoopsum foo lor barr ipsum foo dolor foo
^1 ^2 ^3=bar ^4 ^5