My check engine light keeps coming on everyday for a while, and then it will go off. When I check it the code (while the check engine light is on) is 444. Which means no faults stored. Does anyone know if this is correct, and what I can do to get the check engine light to quit coming on?

Try this:

Take your gas cap off. Very lightly lubricate the rubber inside the cap with some petrolium jelly. Put the gas cap back on tightly. Put the key in position 2 for 20 seconds and take it out. Then start the car.

HTH

you should also try cleaning the MAFs if they haven't been cleaned. My 750iL did the CHECK ENGINE light also and after the MAF cleaning, it went away. Does the light go out immediately when you increase rpms?

Had a similar problem finally sorted out as dirty air filters.
Worth a look as they are only $6.51 at Autohausaz
http://www.autohausaz.com/search/product.aspx?sid=z1tymw45rohnfh2rbzyqunra&makeid=800003@BMW&modelid=1013106@850I&year=1991&cid=22@Fuel%20%26%20Air%20System&gid=6192@Air%20Filter

Had a similar problem finally sorted out as dirty air filters.
Worth a look as they are only $6.51 at Autohausaz
http://www.autohausaz.com/search/product.aspx?sid=z1tymw45rohnfh2rbzyqunra&makeid=800003@BMW&modelid=1013106@850I&year=1991&cid=22@Fuel%20%26%20Air%20System&gid=6192@Air%20Filter
You let them get THAT dirty? I did it this year, the cause was "sometimers"!

Actually it was a case of sheer stupidity on my part. 8-)
My stock air filters on my somewhat neglected #2 winter beater E31 were dirty and I had no new ones on the shelf so I put in my "previously removed as unacceptable" K&Ns temporarily and promptly forgot about them. Some time later I started getting CE light and in diagnosing realized the error in my ways. Pulled out the now very dirty K&N's and tossed them into the dumpster which is what I should have done with them in the first place. CE light never came back. I now stock 3 sets of stock Mann air filters on my shelf to support my fleet. Lesson learned.

Had a similar problem in addition to a rough idle and several codes. Threw out the oil pregnated K&N air filter, cleaned the oil coated MAF with MAF cleaner. Car now runs smoothly with out codes or CEL.

Yup - worth saying one more time - If you have K&N filters, GET RID OF THEM!

to me it sound like something related to the MAF... it may be dirty or need a rebuild