I'm not even certain they would be 'alive' in the normal sense of the words, they would be more like a plant than an animal, and plants, in ideal conditions can live to be extremely old indeed. Now, take a 'plant' that is engineered to grow into a specific shape, genetically coded, with an external technology to ensure that mutation doesn't compromise the design, not too difficult if you are capable of designing a genetic structure from the roots upwards, as it were.
The 'seed' itself takes care of controlling all the functions to grow the ship, you only have to supply materials, it's an enormous initial expense to create the genetics, but once you have the 'code' for creating the seed, it's a massive saving on building understructures. Once the structure has grown, then further technology is connected to the structure, such as armour etc, or possibly even grown there as an exoskeleton similar in fashion to the suits that Shivans wear, only more rigid. The ships are still piloted, they are not sentient, they have no nerves, so they can't feel pain or react in any manner they are not instructed to, they are still machines, but biologically created ones, not manufactured.
The advantages are actually multiple, which is why modern science is trying so hard to do this kind of stuff, as long as you have the material, you need minimal building facilities, which is handy for frontline deployment, ships would be unlikely to be self-healing as such, but certainly, once out of the battles, genetic coding could make repairing them a lot simpler than having to dry-dock the ship etc.
Edit: I'm not saying this is how they were made, I'm saying if they were biological, this is how I think it would work. I could even go on to suggest that those 'Comm Nodes' were ship seeds that were receiving/relaying construction data from somewhere, after all, it's entirely a hypothetical conversation in the first place.