Some laptops will lose performance without the battery installed. My mac specifically warns about this if the battery is removed (while it is running) and then is on the AC unit alone. You can remove the battery if you wish, it won't likely add any longevity to the batteries life span. Certainly charge cycles can lower battery life span, so if you are constantly draining it and recharging it, the life span could be shorter, however in your case I would probably just leave the battery installed. Leaving a dead or near dead LION battery unplugged for too long can cause it to lock or go into protect mode due to low voltage, I had this happen on a mac battery that I left out for about 8 months, in my case the battery was actually fully charged when I took it out, I am not sure how it managed to drain over 8 months to a critically low level. I had to get a new battery after that, I just leave my new battery installed now and after 2 years it still works about as good as it did new. I expect to get about another year out of it maybe 2 if I am lucky.