Camera takes a long time to properly focus sometimes

[KmH]

AF systems usually work by detecting contrast. In low light, there just isn't much contrast...

I was under the impression that all the SLRs worked by phase detection rather than contrast detection. Am I incorrect?

No.

Today, many DSLR's use contrast detection AF when in live view mode.
In live view mode the main and secondary mirrors have to be up out of the light path to the image sensor, so the phase detection AF module in the bottom of the camera body cannot be used. The main mirror has a section that is 50% transparent so light can go through to the secondary mirror and bounce the light down to the phase detect AF module.

Also for the OP, there are some scene situations where AF does not work very well. See page 135 of your T3i Instruction Manual.