2001 Suzuki XL7 won't stay in 4WD

This unit has a rebuilt automatic transmission with 30,000 miles on it and the original, untouched transfer case with manual transfer case shift-into-4wd lever. The shift pattern for getting into 4wd is: 2wd at bottom right; 4wd-High is straight up from 2wd; 4wd-low is left of 4wd-High and then up.

Issue that has been occurring sporadically for a couple of winters but is now happening with much frequency:

a) after shifting into 4wd-High from 2wd I see the 4wd lamp illuminate on the dash and (most importantly) we can feel that 4wd has engaged as the front wheels now have power (e.G, fishtailing on slick surfaces is eliminated; vehicle is obviously pulling with all 4 wheels as we go up a hill)

b) I continue in 4wd-High but when starting from a stoplight or going up a grade it is obvious that only the back wheels have power (e.G, vehicle has reverted to 2wd; fishtailing resumes; car does not pull up the grade; rear wheels are spinning-out) BUT the 4wd lamp is still illuminated (no flickering or on/off) and the transfer case shift lever does not "appear" to have moved from the 4wd-High position - it is definitely not in the 2wd position

c) I put a hand on the transfer case shift lever and nudge it up a few millimeters and can feel it push past a detent and the 4wd-High re-engages: fishtailing stops and resumption of 4wd pulling power is obvious.

d) now I drive while keeping a hand on the transfer case shift lever and when accelerating or starting up a grade I feel the transfer case shift lever nudge down and out of 4wd-High as the transfer case slips back into 2wd i.E, repeat of items b) and c) from above.

Vehicle otherwise performs wonderfully when it stays in 4wd-High or while we are in 2wd (which is 95% of our driving); I don't know if this occurs with 4wd-Low as we have not encountered conditions warranting the bull-low mode.

Any suggestions would be appreciated.