I took a view on the use of the title "ban". It was in the critical time (15th/16th century) the highest title one could get in the three regions Slowenia, Dalmatia and Croatia. A sort of premier minister, one highest official in all 3 regions.
Wikipedia has a list of the bans.
http://en.wikipedia.org/wiki/Ban_of_Croatia
The name Frangipani appears in the following years.
1391–1393 Ivan Frankopan of Krk, (died 1393), also at the time the Ban of Slavonia (as all, who follow)
...
(1406-1408
Heinrich II von Cilly (father of Friedrich II., grand father of Ulrich of Cilly))
...
1426-1432 Nikola Frankopan, Son of ban Ivan Frankopan
(a pause of one year with no ban at all)
1434-1437
Stjepan Frankopan ("our Stephan, who married Isotta"), co-ruled with Ivan Frankopan 1434-1436
(a pause of 9 years with no ban at all)
(1446–1450 Ivan Hunyadi)
(a pause of 3 years with no ban at all)
(1454–1455 Ladislav Hunyadi
(who killed Ulrich von Cillly) )
1456-1458 co-Ban Nikola Frankopan, Son of Ban Nikola Frankopan
...
1575
Krsto (Christopher) Frankopan (Frangepan) ("our Christopher, who married Apollonia") (died 1527) Grandson of Ban Stephen Frankopan
********
One can see, that a period of 32 years (1426-58) was dominated either by a Hunyadi or a Frankopan ... this is unusual for the list of the bans (as you can compare).
The break of 9 years (1437 - 1446) with "no ban in three regions" started with the death of emperor Sigismondo, who had been an Hungarian emperor. That's likely not an accident, but just indicates a general period of Hungarian confusion. The state found more stability with the election of Matthias Corvinus, son of John Hunyadi, in 1458. And that's just the year, when the Frangipani influence took a long pause.
Heinrich II. of Cilly had been of great help in the period, when Sigismund developed from a King of Hungary to Emperor Sigismondo. So Sigismondo married his daughter Barbara (1405), which happened to be a rather unlucky choice, cause she didn't get a son.