What was the cause of the decline in remittances sent to Pakistan between 1982 and 2000?

Perhaps more enlightening would be the reason why Remittances increased so much from 1976 to 1982, and then cooled off.

1977 was the year of a military coup in Pakistan (and the imposition of Martial Law), that was also, it appears, the beginning of deep structural socioeconomic changes. In such situation it is not uncommon to see a wave of emigration, among those that do not "fit well" in the new situation. But this rarely means that the emigrants severe all ties with the country back home, usually some family is left behind. Hence, increased Remittances.

In 1985 Martial Law was lifted and elections were held, and this could explain the downward trend.

So I would look into the emigration/repatrization flows in Pakistan during that era, coupled with the political situation and any economic reforms.