It's probably just your fps. If your game does not match the minimum or maximum requirements to run GTA San Andreas smoothly then your game will have performance problems.Try this website, "Can You RUN It".
http://www.systemrequirementslab.com/cyri
My game doesn't even match the minimum requirements but I'm still able to play.
My trick is to remove anything running in the background (Example: Firefox, Skype). I also run my GTA SA in 800 x 600 or lower, you should even try x16 with frame limiter off, no shadows, no anti aliasing. I have a few modifications but only skins or weapons that fit with the game itself, not HD mods. Anyhow, It can also be where the server is hosting from that causes your connection to be slow at a certain server.
You can try downloading Game Booster, where it disables background programs to make your game have better performance you can even defrag your game files or your computer. I recommend early versions of Game Booster that you can find on the internet, not Game Razer that's the newest one out.
I get this "freezing" thing a lot as well sometimes only in certain servers like West Coast Life whenever I'm riding as a passenger on the back of an NRG, or like you said in an important chase.