My bed room has 8 receptacles. Recently I noticed that only half of which are working and the entire room is on a breaker by its self. The breaker never tripped. Can someone please tell me what could be my problem?

Most likely there is a loose wire connection at one of the outlets, usually at the last working outlet on the circuit.

You will probably find the wires are pushed into small holes on the back on an outlet, this type of connection is popular with getting loose. Change any connection like this to wrapped around the terminal screw connection.

Re check breakers again
"Problem(s)" Open neutral / open hot /switched neutral, loose connection in wire nut or bad outlet in series. OR
Are any outlets on a split? One outlet as a continuous hot and the same outlets is on a switch? If so back to different Breaker tripped/switch bad/ open neutral in switch loose wire in wire nut ( nuterals)
To check Dead outlets, Breaker off. Pull covers plates. Use electrical tester to confirm all outlets off but always assume its still hot until you KNOW its 100% off and we don't know that until the problem is solved!
Unscrew outlets covers and look for a bad/ loose wire screws on side of outlets.
Then carefully let outlet hang out of wall, wires still on outlets, inspect all wires. If you see wire nuts unscrew and check for loose wire. If outlets also have push-ins wires in back of outlet gently pull to confirm good connection If everything checks out now have an adult guard outlets for safety ( kids around house) and turn breaker back on. Take tester leads and carefully check all exposed screws of hanging outlet to see power on both hots of outlet. One more situation. One of the outlets that in the series circuit of that room could be the feed for the rest of the dead outlets. So it's a krap shoot check outlets also on either side of those outlets and no hot from one of them could kill the other outlets for the feed. Also its possible theses outlets are fed from adjacent room Or a junction box in attic that drops a feed to those outlets. Sorry for the long descriptions I tried to cover most all.
Basically If you find the feed to outlets and go from there and confirm breaker possibilities I don't know how old your house is that's make a difference here on knob and tube Junctions box's hidden/ floor/ attic/ basement/ even ran through/past light box as junction There's a couple of possibilties but try these first. AGAIN Always assume wires are hot until 100% sure not!
Hope this helps
Merry Christmas!!
Signed 21 Boat

Still having problems with your outlets?
21Boat has all the tough options handled.
You might try just checking to see whether half the outlets are switched. Not a real common installation practise but often in a bedroom where you may want a switch to control a plug in lamp. Half of the outlets are hot all the time and half are switched, all on one breaker. This is done by carrying the hot through each outlet using 3 wire. Sometimes the outlet side tabs are broken off and the top plug on one outlet is off (switched) and the bottom plug on the same outlet is hot.
I've come across both scenarios over the years
(Learned this lesson the hard way back in the seventies when I filled up a water bed next to a switched outlet. Oh S___.)

I got to go with TK, Last good, or first bad receptacle.
You could use an extension cord for reference with a meter to see if it is the hot or neutral failing. Then you can pay special attention to the hot or neutral.