The A1000 was released in 1985, the same year as the NES was released in America. It was a huge leap in capabilities over it's contemporaries.
But their massive lead was slowly whittled away by technology improvements. In 1992 they released AGA, which was barely twice as good as the original A1000 chip-set, while the IBM PC had innovated all the way from 4 color CGA, though EGA to VGA/SVGA with CPUs which were fast enough to any 2d (and increasingly 3d) effects in software.
Commodore really needed to get AAA out the door by 91 to hold onto their lead.
Doom was probably the final nail in the coffin, you simply couldn't implement it on the Amiga chipset due to it's planar graphics.