It seems like the city that doesn't sleep shuts the bars up pretty early. Whatever the reasons are, we just have not many options for the next 4 hours before the sun comes up. Fortunately there a few bars that remain open till dawn.

With the recent enforcement of the "current law", all places are being closed at 2 am. Unfortunately, you can't party all night long now. You can still get beer past 2 am at some hotel coffee shops. Try places such as Grace Hotel's coffee shop, they are opened 24 hours a day.

Here is the list:

Thermae (between Sukhumvit Soi 13 and Soi 15, at the basement of Ruam Chit Hotel).
Closes at 5 or 6 am, but some times, as early as 3 am (that's when the police do their round-ups)

~~Concept CM2~~ (basement of Novotel at Siam Square)
Closes at 3 am.

Eden Love (Patpong Soi 2, next to KFC)
Closes at 5 am

Nana Disco (ground floor of Nana Hotel, Sukhumvit Soi 4)
Closes at 5 or 6 am (again, could be earlier depending on the police)

If you are looking for some company, for a short duration or for the remainder of the night, check out this place:

Siam Hotel Coffee Shop (Petchburi Road, next door to Mona Lisa)
Girls generally do not speak much English, as most of the clientele are locals. That does not mean, you can’t get lucky there.