The path in which you could take Nixon in order to get him elected in 1980 is not necessarily set in stone. Nixon was well known in OTL for possessing the almost superhuman ability to make a political comeback. In OTL, by the time of his death, he was again a respected statesman and was a trusted ear to President Clinton and made multiple trips to Russia as a dignitary multiple times after the fall of the Soviet Union. So, saying he must remain relevant isn't all that necessary, what is necessary is how we were to make Nixon relevant again ITTL.
The approach taken would also change what Nixon we were to get in this alternate 1980. Do we want a more moderate Nixon? More Conservative? less paranoid? more paranoid?
The way that gives us a less paranoid Nixon resembling more of the man as he stood in 1960 is to take the route that gives him less defeat than OTL and less distrust in the media. To do this, we grant Nixon an election victory in 1962 over Pat Brown in California. Now, it is also known that Nixon much preferred Foreign Relations as a topic than domestic. While this is not to say he viewed one as more important than another, Nixon excelled in foreign relations and would prefer a role that allowed him to have influence there. Therefore, I do not see Nixon running for another term as California's governor. From there, it would depend on the political landscape of the time on what he did.
To get him to run in 1980 instead of '68, '72, or '76, we will probably need him to sit out in 1968, and have a Republican victory in '72 that then folds in Horribly allowing for another Democratic victory in '76.
In my planned timeline, that Republican in 1972 was to be Alexander Haig who suffers from a scandal worse than Watergate. Nixon manages to remain untainted from the collapsed administration and this Nixon would be one respected by the media for not being involved in a scandal. A Nixon like this, would have had executive experience and foreign relations experience; and his surviving the collapse of the administration would put him in the prime position for a run in 1980.
But like I said, there are probably more than 40 ways to get Nixon to 1980 and win by a good margin. But each way will give you either a massively or slightly different Nixon.