Tony Starks's drinking ultimately required Rhodey to become Iron Man
in February 1983's issue #170 of The Invincible Iron Man.
Details and above scan via this site.
When I got into comics a bit later in 80's - Tony was mostly recovered - but Rhodey was still
frequently piloting the suit. They were kind of like co-Iron Men. And of course Tony was tinkering
with various next-gen tech that would lead to War Machine, as well as his own upgraded suits.
Additional panels via this super Rhodey Tumblr