Does it randomly crash anytime in the middle ages, or does it always crash at a given spot/time... like when a new tech is discovered (either by you or any other civ?).
One of the leading causes for crashes mid-game in a mod is something not being right with a unit when entering a new age... and this doesn't necessarily mean YOUR civ... it could be any of the AI's civs that just enters an age. You could be 20-turns into the Medieval age, when one of your AI opponents just switches from Classical to Medieval and that could cause the game to crash when that AI civ makes the switch to medieval (the two most common mid-game crashes occur either in the switch to medieval, or the switch to industrial age, as both cause graphic changes).
It's also quite possible that this bug has been there for a long time, including in v3.13 of your mod. Let's say the problem is with the Zulu switching to Medieval, and you never play the Zulu, and they never seem to randomly show-up in your games... you could have played three dozen games in v3.13 with your mod to completion and never had a problem because the Zulu were either never in your game, or eliminated before they reached Medieval stage. It's entirely possible the problem has existed for awhile and you're just now noticing because it's the first time in awhile the Zulu have reached Medieval (once again, I only use the Zulu as an example, not saying they are your problem, it could be any civ).
I had a problem that lasted for about 5 or 6 versions of my mod that I never caught-on to because the problem was with the Mongols and Turks entering the Industrial age... those two civs were either never in my games or were eliminated before the industrial age, so I never caught the problem, though others kept saying my mod would have late-game CTD problems... I couldn't pin it down until I saw the problem myself.
You might try going into your Save Game right before the crash occurs (assuming it occurs at the same spot) and try figuring out who's switching ages from classical to medieval (or if somone is ahead of you and switching to industrial). Also, take a list of what civs are in your game and try each of them in the WB of a new test-game. Give them Medieval techs and see if either the game crashes, and/or check the Civilopedia after jumping them to Medieval and see if any units in the Civilopedia are missing (if there is a glitch with a unit, the Civilopedia will often tip you off by removing all units listed alphabetically after that unit with the glitch in the civilopedia). Check this in WB for each civ you suspect and/or is in your current game. This is often a problem with a civ jumping to a new tech/graphical level like Medieval or Industrial.