Well it's not selectively random. It just eerily feels like the game knows exactly how to annoy you. That's probably because each ship is vulnerable in several different ways, and even if you manage to improve a few things you could still have a big weakness or more than one.
The Basilisk is a superpowerd ship in the mid-late game but it is weak as a kitten early on. Some games you are going to lose period. But you should not allow the game to frustrate you by refusing to let you complete your ideal build. The game doesn't work like that. You are not playing a flexible and adaptible Kestrel. The Basilisk must be played to it's strengths. That means don't go shopping for weapons, concentrate on beefing up teleporter and medbay.
With enough combat experience Mantis can rip apart enemies even if they are being healed by a lvl1 or lvl2 medbay, so you dont need a weapon to disable it. Or you can manage to sneak someone in there to damage it. A lvl3 teleporter is fairly cheap and recycles very fast. Your first boarders can run circles around the enemy to preserve health and then be joined by a 2nd boarding party. You can stretch the defenders thin so they can't possibly respond to everything, and if you can knock out their medbay, you win. It's harder to do with few boarders but 3 can do it. Sometimes you will have to abandon your prey and leg it.
AI ships are a slight annoyance, because you cannot get any scrap from them unless you have great patience. To defeat them you will need a lvl2 tele. Buy it, it's cheap and recycles in time to recover your boarders before they suffocate. Board the weapons room and hack away. Return to your ship to heal then repeat. At this point you can jump away or keep damaging enemy systems. When a system is destroyed the ship will take 1HP of hull damage and since AI ships repair themeslevs, they can be destroyed. Once you wittle it down to 1 HP, use a boarding drone to deal the final blow. But it's less annoying just to cut your losses quickly and leg it.
Zoltan ships. This is why you want to upgrade engines on a Basilisk. This and hazards. Just forget about it, take your lumps and leg it as fast as possible.
tl;dr
Don't play the Basilisk like a Kestrel. You must adapt to this ship, it's ways and it's weakneses. Happy pirating.
Needless to say, all burned to death in a gloriously horrible celestial pyre.