Triumph, unlike the others you mentioned, never never went completely out of business and has produced motorcycles every year.
Well... it looks like PEAK production numbers for Triumph between 1983 and 1988 were 14 a week, for about 728 a year.
Based on those numbers, the Gilroy Indians were a HUGE success with about 8,500 Chiefs made between 1999 and 2003.
While it's true that Triumph continued to build bikes, it wasn't exactly doing a gangbusters business. I'm guessing some of that heritage 1902 DNA was falling between the cracks in those lean years of the 1980s. If you want to hang your hat on that continuous Triumph DNA, make sure it's a small hat.