I have a 40-year old SP who has been with my franchise FOREVER.  He actually had a solid year (4.40 ERA, about 200 IP) this year and he is asking for $2.4 million to come back for his age 41 season next year.  My team is rebuilding and I would like to bring him back, but not at the $2.4 million he is demanding for next season.  My question is, if I don't resign him for next season at the close this year, will he automatically retire at the rollover given his age of 41?  OR will he go to free agency next year regardless and not retire until the following rollover after that if he goes unsigned next year?  

No way to definitively answer that.  He may retire, or he may not.

Considering his age (and not seeing the player), he's likely to be in a severe decline with respect to durability/stamina, so expecting another 200 innings might be a stretch.  His skill ratings are also likely to be declining, so I would also expect 4.40 ERA to rise.

My opinion - the pitcher you're referring to was a little lucky to get that ERA in the first place this year.  His ratings will continue to fall, and he really won't be ML quality next year.  I'm as guilty as anyone when it comes to hanging on organizational lifers, but I think you're better off letting him retire.