Eight times, the members of the Apekin family have applied to renounce their Soviet citizenship and leave the Soviet Union for Israel, and eight times they have been refused.

Last Oct. 22, as the summit meeting between President Reagan and Soviet leader Mikhail Gorbachev approached and hopes ran high, they applied again, and that time were asked to pay 700 rubles ($910 at the official rate of exchange) for each adult member of the family -- 2,100 rubles ($2,730) in all for Vladimir, his wife Katrin Skazkina and daughter Katya.

Yet, despite this unusual payment -- which they took as a sure sign of imminent exit visas -- the Apekins have not received permission to leave.

Now Vladimir, a 49-year-old former marine biologist, is suffering from a severe case of arteriosclerosis. According to his 26-year-old daughter, Katya, he needs immediate surgery.

According to Katya, doctors here have told the family that they lack the high-quality artificial blood vessels needed for the operation.

"The doctors told us, 'Do everything you can,' " Katya said, although she said the doctors had no idea that the family had already applied to emigrate to Israel.

Katya and her mother Katrin, 49, went on a hunger strike on April 1. Katya stopped on the 18th but says her mother is continuing.

Ever more desperate, they sent off a batch of telegrams -- 12 in all -- and letters -- 80 in all -- to everyone from Gorbachev to delegates to the 27th Congress of the Soviet Communist Party, pleading for permission to go to the West for treatment.

"Everything that came into our heads, we did," said Katya recently. "We've done it all."

After almost seven years of waiting, the Apekins -- a Jewish family originally from Vilnius, in Lithuania -- had almost grown used to their fate as refuseniks. The parents had lost their jobs in 1982, but Katya, who has a daughter, works as a ceramics artist.

When they applied again in October, they thought their chance had come. Other acquaintances in Moscow had left before the summit. And they had handed over the money -- a major sum in Soviet terms where the average monthly salary is 200 rubles ($260).

Six months later, the uncertainty is still there, and Katya is convinced it has affected her father, who has heart and lung troubles in addition to arteriosclerosis.

As she launches her appeal, joining the many other refuseniks who see hope in attracting attention in the West, Katya despairs. In her view, not even another summit would help.

"One comes, then another and nothing changes," she said on a wet spring day not long ago. "First you hope for spring, then for fall, then some meeting -- and each time, everything comes up empty."