The game becomes sluggish in late stages, when there are many ships.

[user12334]

There gets a considerable latency (0.5 to 1 seconds) in any actions (such as dismissing reports, opening windows, ordering build, etc.).
It is worth to profile the game, probably it's easy to find bottleneck(s) and fix.

[sven]

There gets a considerable latency (0.5 to 1 seconds) in any actions (such as dismissing reports, opening windows, ordering build, etc.).
It is worth to profile the game, probably it's easy to find bottleneck(s) and fix.

How large is the map you're playing on? (Would you upload a save?)

[user12334]

There gets a considerable latency (0.5 to 1 seconds) in any actions (such as dismissing reports, opening windows, ordering build, etc.).
It is worth to profile the game, probably it's easy to find bottleneck(s) and fix.

How large is the map you're playing on? (Would you upload a save?)

It's 85 stars. Here's the save: https://yadi.sk/d/jE7jR-3N3WNUSe.
Though I had lags even worse than that on older games, but I didn't keep the saves.

But for the better profiling material I would suggest you generate some 500 stars galaxy and let some 20 AI players run for 500 turns. Such save should lag pretty good.