Well, 30 years ago we had something called Irangate, now better known as the Iran-Contra affair. In August 1985 the Reagan Administration secretly started selling TOW and Hawk missiles via Israel and arms dealer Manucher Ghorbanifar to Iran (which was then at war with Iraq), partly with the intention of signalling US readiness for what the President called "a new relationship", partly to secure the release of US hostages held by pro-Iranian groups in Lebanon.

The scheme (which had meanwhile acquired another angle with the use of the profits to bypass Congress's block on funding Nicaragua's right-wing contra rebels) fell apart following its disclosure in November 1986. Various Administration appointees were later convicted of perjury, obstruction or withholding or destroying evidence, but pardoned by the elder Bush.

And that sorry affair was the high-point of relations in the period. Within a year the US was attacking Iranian oil installations; then came the downing of Iran Air flight 655.

Why did relations stay so bad? US memories of the 1980 Embassy epic and the 1983 disaster in Lebanon, Khomeini's hard-line stance on foreign relations, and mutual suspicion and short-sightedness. Khomeini's death in 1989 seems a lost opportunity for a new departure, but by then the world was changing and US interest in minimizing Soviet influence (cited in the Tower report as a motivation for the arms scheme) soon no longer applied.

The 1987 Tower Commission report on the arms affair is summarized at http://www.presidency.ucsb.edu/PS157/assignment%20files%20public/TOWER%20EXCERPTS.htm.

You might consider x-posting this question to /r/politics or a sub that discusses US foreign policy: this subreddit has a "20 year rule" against current affairs, so people here will be able to address only 1979 to 1996.