If plural of "index" is "indices", why is plural of "regex" not "regices"?

Well that's English for you.
Just like plural of mouse is mice but plural of house is not hice.

Well, index came from Latin while regex came from the 50s.

@Alice This is the only correct answer

Because you should only have one regex

Index is Latin as @AlexDeLarge said so it has a plural of indices.

Regex is a shortening of regular expression, so plural of that is regular expressions.

Shorten regular expressions and you get regexes to quote from the Wikipedia talk page on the word regex

"Not regexs because that's irregular for no reason (we don't write boxs or hyraxs). Not regex's because that would be a possessive. Not regeces because it isn't from Latin (which would anyway probably be regices; compare index/indices). Not regex expressions because that's the plural of a different noun phrase. Not (regex){2,} because that's... just silly. No reason why it would be regex either. So it's regexes or, humorously, regexen."