There are many portuguese explorers that went to the west, and most of them survived.
Diogo Teive for example in the returning trip discovered the Corvo and Flores islands of Azores.
Actually Columbus' voyage was pretty safe and easy, it's almost a straight line, the portuguese explorers after say the 1460s were pretty confortably with open sea voyages and those were the easiest.
Some claim that in the Fra Mauro map of the 1440s, the sea to the west that is called Mar de Baga ("Sea of Berry") is actually the Sargassum sea with the "berries" being the knobs in the sargassum seaweed.
D. Brites, the wife of Prince Ferdinand, Duke of Viseu, was kinda the regent of her son Diogo Master of the Order of Christ after Ferdinand died, and she had the atlantic islands as her "domain", and she did send or allow several voyages to the west.
We know very little and specially after the 1470s the secrecy of the portuguese explorations went over the top as Prince John (future John II) took over the Discoveries "folder".
Even Bartolomeu Dias' voyage is known a little more than a footnote because of this, and this one was a really long and dangerous voyage not only because of the distance but also because he was forced to be close to the coast to check ou the african coastline.