What you're describing seems to be an interface bug, or as InfiniteVoid points out you may mistakenly be playing in cinematic mode, which is pretty well only useful for screen capture; it's pretty well impossible to actually play.
I'd also like to point out that you are using both expansions.
I took a look at the replay; it begins over an hour into the game, and the AI had already accumulated a substantial advantage by this point. A veteran could still pull this off, but this is pretty much unwinnable for a beginner. The AI has a much larger empire, a much better economy, and some very high-level capital ships (that level 6 Marza in particular is a major threat). I'd be much more interested in looking at what got you into to this situation. I highly suspect your pace of colonization is much too slow, which means I'm most interested in the first half-hour of the game.
This is a screenshot of the map I took while I watched your replay, for others to see:

It was taken at about 1:40, and at this point it looks like the AI is on the verge of making a killing blow, since your failed rush at a starbase got your fleet killed.
Your assets:
4 planets (~25% developed)
202 /690 fleet supply
3 capital ships (levels 3,3,1)
0 starbases
Savings: 13000 credits, 1200 metal, 1400 crystal
Income: 19 credits, 2.2 metal, 3.3 crystal
Enemy assets:
7 Planets (~75% developed)
476/500 fleet supply
4 capital ships (levels 6,4,3,1)
3 starbases
Savings: 2700 credits, 1600 metal, 600 crystal
Income: 40 credits, 5.6 metal, 4.8 crystal
This really reaffirms my theory of slow colonization; the AI colonizes faster, giving it more income, which it then uses to develop its existing planets faster. Basically you get an effect like compound-interest, and a small initial advantage for the AI turns into an overwhelming economic advantage over the course of an hour. By the point at which the replay starts, it's much too late to reverse this advantage.