I think they started making poor decisions in what kits to make.
(1) Their television kits were far better than Zenith. I remember seeing rural installations where perfect color from 250 to 300 miles was normal.
(2) Entering the robot market was a mistake. Robot technology was far too primitive at the time to be of any use.
(3) Entering the computer market was a mistake. PC's would soon go to Windows. "Kits" would have to consist of motherboards and disk drives and cards. Not very interesting or challenging.
(4) Entering the educational market was a mistake. Heathkits were always educational. And fun. Not so the educational kits.
If they had stuck with their core of things they did well - hi-fi / stereo gear, ham gear, TV, test equipment I think they would still be around. Those other lines drew resources away from their core business, the number and quality of kits declined.
There is no reason why they couldn't have done kits that included 1206 case surface mount resistors. Those are large enough and robust enough to be soldered by an amateur. Through hole IC's are fine for soldering. If anything, the advent of IC's would have made more kits easier for complete novices. If a part was only available in surface mount, on a fine pitch - Heathkit usually gave the hard to assemble pieces (like FM front ends) as pre-assembled modules, and just treated them like a part in the instructions.