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As a GM is it unfair to secretly protect one players character?

I have recently started playing (as GM) tabletop RPGs after a several year hiatus because I was no longer finding it fun. My current game has been running for about 6 months and I am enjoying it and my players seem to also be enjoying it.

However I have an issue with one player. This player gets upset when ever things don't go the way they want with their character. For example if their character (a fighter) missing too many times in a row. It gets even worse if the character starts getting low in hitpoints and the player feels like the character is threatened. I personally find this kind of behaviour on the part of a player to be stressful. I have started fudging die rolls in the characters favour occasionally, just to keep the peace.

I have been playing with this player on and off for more then a decade both as another player and as GM/DM. She is the type of player who always plays a similar character - a fighter. I had always thought she just plays because her boyfriend and most of her friends play (she played D&D 3e for years but still never seemed to understand many of the rules) until she told me it is one of her primary forms of stress relief (she has been having a hard time lately).

My question is this: Is it unfair to everyone else if I just keep fudging stuff for this character (not too much, just enough to make sure they don't die or anything) just to save myself the headache and make the game smoother and more enjoyable for everyone? I don't want to ask the player to leave the game because that will cause me problems with my social group. I just want to have fun and enjoy the game and I want everyone else to have fun as well. Obviously the other players get a bit protective of their characters but no one else is even close to this intense and upset about it.