Its actually a surprisingly secure job. Majors was about .500 overall after his first 6 seasons. His career SEC winning percentage (for 16 seasons) was 57%. Most of those wins came against Vandy, UK and Ole Miss. Majors was 4-12 against Bama, 6-7-2 against Auburn, 1-4 against UF and 1-3 against UGA for a combined 12-26-2 record against good SEC teams. The irony is that UT ran off Majors at the peak of his success rather than earlier in his career when an ouster would have seemed more justifiable.
Battle managed to stay at UT for 7 seasons, but was .500 or worse in SEC play in each of his final 4 seasons (10-13-1). He inherited a program that was immensely talented and had beaten Bryant and Bama 3 straight times. His last two teams (75' and 76') did not receive a bowl invitation.
Fulmer comes along in 93' and elevates the program winning an amazing 45 of 50 games from 95' through 98'. UT only lost one game to a SEC West opponent in 5 years from 95' through 99'. Only 90's powerhouses like UF and Nebraska could beat the Vols during this time. After 98', the program recedes into a good, but not great, SEC program. The Vols have lost 4 of the lost 5 bowl games, and are riding a 4 game losing streak to UGA. The occasional high (a win at Miami) seems to amply mitigate numerous and recent lows (Peach Bowl fiascos, losing 41-14 to UGA).
IMHO, the program is approximately where it was when Majors left (except that UT now beats Bama). When you consider that Majors was at UT for 16 seasons, and that Fulmer generated UT's first official national title since 1951, a picture unfolds that Fulmer will probably be here about as long as he wants to be, absent a complete freefall. Simple logic would suggest that if he won 1 national title, he is entirely capable or repeating such a feat or coming awfully close (see 2001, UT would have played Miami in the BCSCG had it won the SECCG). However, I have my doubts considering that UGA has raced past UT in short order and UT now struggles to win games against mediocre opponents.