I don't know how well T-Max developer keeps, but opened for a year is rather long.(posted 8071 days ago)That said, I don't think you have a developer problem. You should get similar densities throughout the roll. If not, you have either an exposure problem, or something that is preventing the chemistry from getting to some of the film (perhaps poor agitation). Without seeing the film, it is rather hard to tell. If you would like for me to look at the film to try to determine the problem, send me an e-mail to david.carper@ilford.com and I will give you instructions on sending it to me.
David Carper ILFORD Technical Service