Question: I used to own Dewalt DWE575 (*7-1/4, 15 amp*) and liked it quite a bit. Unfortunately, my garage got broken into and it was stolen.

I bought a used DWE575SB, which is similar, but with electrical brake.
I put on a new blade but it cannot cut through a 2x6 without getting stuck.

The other day I tried to cut through a 1x12 pine board and it couldn't complete the cut. I don't recall the previous one had such issues.

Can I conclude that I bought a lemon and it's at the end of its life?

What other signs should I look out for before spending money on a new saw?

Answer: 
After the saw has failed to complete a cut quickly unplug the power, remove it from the work piece, and test whether the blade still turns freely. That'll check whether there is some drag that develops while the saw is in use. If so, repair might not be economical.

Assuming that it's a normal AC or universal motor (ie, not a brushless DC motor) then it's worth taking a few minutes to inspect the brushes. A motor can start acting weird when the brushes are nearly worn away. A new set of brushes is usually an inexpensive repair.
Make sure you don't have the blade in backwards. Every circular saw on Amazon has a few one star reviews from people that put the blade in backwards.