So, your drain cleaner doesn't seem to be working as advertised. Chances are, you're not using it as advertised. Anyway, water remains in the trap preventing sewer gases from rising into the house. These traps are also where debris can collect and clog the drain. A trap can be unclogged several ways.
Drain cleaners work great here.
You could use a plunger, forcing the debris further down the line. Plungers Plungers work great on P-traps, but are not very effective on the can type of trap. This is a good place to explain how to get the most oomph for your plunge. While I'm sure you know the idea behind a plunger, which is like a giant suction cup, is to momentarily build air pressure above the clog pushing the debris on down the drain. To build this pressure, the path between the plunger and the clog must be airtight.