They could easily destroy my starbase but after several turns of fighting they simply stop attacking and just sit there. Internal systems were down on some ships but not all and they could've finished the base. I've added a save. Just end the turn and a fleet (1BS, 3DS) will attack the capital system. Fight them the best you can (I targeted the BS), you should get overwhelmed but the enemy will eventually stop attacking and cause a stalemate. It's a bit iffy because the 1st time my base had Neutron Beams but the second time I tried it "rolled" Ion Cannons instead so the situations could end up being a bit different.
Thanks a lot for the bug report and the save. There was a bug in the AI calculations that caused attacking ships to become more defensive then they should, especially in this particular scenario. I repeated the scenario 3 times, and in all of them I could destroy the battleship and one of the smaller ones but I ended up losing that battle every time. The fix will be up in the next update.