What is the maximum number of dice you can roll in Arkham Horror 2nd Edition?
There is no maximum number of dice you can roll - it is infinite as the rules never explicitly call out a maximum dice total.

Considering the mechanics of the game though the extreme theoretical limit would be somewhere over 70 (but likely less than 80).

In theory....

I don't have the time to go through every card to work it out, but given the example from the rulebook as a basis where Ashcan Pete has 16 dice (it was 13 after accounting for the monster he was facing), we could easily add a further 2 by replacing his .45 Automatic with another copy of Shrivelling, bringing us to 18.

We then account for the fact there should be 48 Clue tokens in the game according to the rulebook (extremely unlikely a player could ever get all of them, but we are talking pure theory here), we are up to 66 dice.

Then considering a few monsters give a positive combat modifier, and some skills give further bonuses, and (it's been a long time so I don't quite remember) there may be character abilities that can add a few more points (situationally or by spending resources), we could push past 70 dice for a single combat roll.

In actuality....

Around 15 dice will do in most real cases, and any player who does stack up a larger hit has the satisfaction of rolling multiple handfuls of dice (and the pain of keeping a running tally if they really want to roll all of them).

My personal copy of the game has 30+ dice, but that is more for spreading them around the table within easy reach of all players, than in the expectation of a massive roll.