It's VERY, VERY strange that you never had any problems with the Medium helicopter since I can Reproduce these issues something like 100% of times!
Are you sure that you're playing on "Expert" dificulty or that you played enough time with the Medium helicopter (more than a simple "5 minute trip").

I always had this problem with this medium helicopter but in previous version if I was very carefull with the helicopter (treat the helicopter like it was actually "made of glass") I could play and end missions with the medium helicopter without too many extensive strutural damage. But now with version 1.04 things are MUCH WORSE, even if you treat the medium helicopter "gently" it will inevitably get damage by itself specially loosing tail rotor authority which is a thing that didn't happen (tail rotor "stuff") in previous version 1.02 for example.

Just try the following:
-> With patch 1.04 installed play a "lift cargo" single player scenario/challenge with the medium helicopter and tell me if you can end that challenge without loosing the tail rotor and at least end it without extensive "strutural" damage!!

Honestly this is so easily reproducible since with the "light" and "heavy" helicopters you don't get that kind of exagerated and unrealitic damage like you have with the medium helicopter!

I've done several missions with the heavy helicopter. I have never had a problem with it, even on "Shakedown" where you need to do a few edge-of-the-envelope type manuevers. I've only ever played expert. Try a large amount of curve on your rudder. I have found that both the heavy and the medium are very easy to corkscrew if I am not careful with the yaw rate.

[Edit: I did try the mission where you sling 3 boxes from one location to another and had no problems.]

I've done several missions with the heavy helicopter. I have never had a problem with it, even on "Shakedown" where you need to do a few edge-of-the-envelope type manuevers. I've only ever played expert. Try a large amount of curve on your rudder. I have found that both the heavy and the medium are very easy to corkscrew if I am not careful with the yaw rate.

[Edit: I did try the mission where you sling 3 boxes from one location to another and had no problems.]

ENGINE
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Medium: flight model would become unstable after rapid slow down, and damage the tail rotor
Improved FXAA and SMAA
Better handling of cases when 3D resolution is not 100%
SMAA uses color edge detection method instead of luma edge
soundLandingGear entry added for helicopter configuration
Landing gear actions did not work in external view
Player gunners are no longer told which weapon to select
MP: spawned vehicles would sometimes get doubled weapon magazines
MP: moveIn*** commands would sometimes show full getting in animations and door animations
Landing gear suspension sound effects were played when the gear was retracted
Battery and starter sound effects were sometimes not playing correctly
RenderTarget fov parameter was not read from config
Underwater RenderTarget cameras would show artifacts on the primary RenderTarget

ENGINE (MERGED FROM OA)
-----------------------
[89898] Fixed: Secondary gunner tracks enemies
[89603] Fixed: A possible crash when textures were loading too slow from the disk.
[89523] Fixed: Crash during engine termination from multiplayer game.
[89361] Fixed: Linux server slow startup

DATA
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M1A2 tank upgraded to full functionality
Takistani AA soldier now has fully functional Igla launcher
Military vehicle radio protocol integrated
Various fixes to all localizations
Initial states for cockpit switches handled better when starting in the air
Cockpit lever for retractable Landing Gear System implemented