Hi, Not Roger - welcome to the forums.
It's an interesting one - I haven't experienced that. The first thing that strikes me is - are you using a joystick, and if so, have you got the landing gear mapped to a joystick button? That's how I have it with my Logitech Wingman. It might be an issue with the joystick calibration (unlikely to be the keyboard unless you also see repeated g's in a wordprocessor, or something like that).
If you haven't got the add-on module FSUIPC then I'd advise strongly to get it and use it in FS2002 - it has many features, one of which is that you can calibrate the joystick much better than you can with the Windows calibration utility.
That might solve your problem - FSUIPC is available as a free download here at this site. Let us know how you get on.