FWIW--I once had a 1963 Galaxy, that one morning would start and idle just fine, but if I tried to get it above idle it would die, instantly. Could start it with perfect reliability, and idle it all day--but try to do anything else--die. In exasperation I called a mechanic friend I knew, this in a mining town just south of the Yukon border in BC. He said 'Your coil has failed'.
'What??--it starts just fine!' He explained that the coil secondary turns are kept separated by a tar-like potting compound; when it fails and more serious than idle demands are made to the coil by increasing the frequency at which they have to supply a voltage that will jump the spark gap, the coil turns can short out either on the case or to each other; the spark-jumping voltage disappears. Went down to his shop and got a new coil--instant (and permanent) fix.
Who knows, it just could apply to chainsaw coils too. Never happened to me before or since; that was in 1971--in Cassiar, a town that no longer exists.
(BTW--if you're scared of asbestos--why am I still alive? My office (exploration geology) was right beside the drier exhaust, that was measured to blow out 6 tons of asbestos dust an hour.)