This game both benefits and suffers from a very long development period. The AI especially has had a lot of work invested into it, and the behaviors have many rules.
Some piloting styles cause the AI to never engage, and how I am naturally inclined to pilot most ships causes this as well (especially small ships). If I just go try to design and fly a ship without accounting for how to deal with runners, nearly all of my battles end as yours do, with zero CR ships trying to kill each other during engine out periods if they have functional weapons (even if I chase them the entire time).
I reported it as a bug a while ago once some of the methods of soloing fleets were removed, thinking it may be an unintentional issue, but I do not think it is, the AI just prioritizes survival.
The key is that the AI will rarely suicide into you, so if you pilot in a way where it never has an opening, and if it closed it would die, it will just back off until it runs out of CR or you do. If they have multiple small ships, that can actually be a winning tactic for the AI, even if very frustrating for the player as they kite you to the time limit and a loss or a stalemate.
The last few games this has not been much of a problem for me, as I never have a fleet without a counter to this issue. The options I have found, in order of effectiveness and ease, are:
1) Be faster. Early game safety overrides and unstable injector are a very good idea, later you still want a couple of small ships built for speed which you can call in to chase something. A hound or hyperion are good choices for this. You simply catch it and kill it or make it stay and fight while you catch it with something larger.
2) Have fighters. A single condor can make you immune to this in the early game, a larger carrier works for later. Most fighters are pretty fast, and nothing can effectively run long term with fighters on it.
3) Greatly outrange the enemy. You may need to disable weapons and target something else, but eventually the AI will nerve up and engage. If it comes well within your range, and you are a larger ship, once you switch to it and open up it will not be able to get far enough away to live. This is mostly a large ship tactic.
4) Massive burst. Same idea as above, but with shorter range and enough dps to wreck small craft very quickly. Just sit, wait, open up, and instantly wreck smaller craft before they can even move away. Be sure to only fire upon a ship if you think you can get a near immediate kill with burst damage.
5) Remain at very high flux. If you can load out a Paragon such that you can survive long periods at 80-90% flux (especially hard flux), the AI becomes very aggressive as it tries to push that advantage. This is a late game tactic where you wreck everything as it closes, and everything tries to close fast (so it is very time efficient). Set the bait, and try to push enough damage to rubble everything before it can hurt you. Many frigates or destroyers at full flux will happily close with you and resolve the fight one way or another if you are at high flux in a large ship.