Riccar Super Strech E21129 364J breaking needles

I believe the number you provided was a serial number and not a model number. When I searched for Riccar Super Stretch it came up with "model 510"

Here's the manual for that just in case it's close enough to your machine that you can get it threaded and such.
http://www.riccar.com/ftp/whitepapers/510-Owners-Manual.pdf

To check the timing of any machine.

Make sure the needle is oriented the way it's supposed to be. Then open the bobbin area so you can see the shuttle hook and needle. (this may mean taking both the bobbin cover off and the throat plate where the feed dogs are)
Turn the wheel by hand until you see that the needle is at it's lowest point of travel. At this point the shuttle hook's point should just be ready to pass the needle scarf. If it is back away from it too far... it is "********"... if it has moved past the scarf it is "advanced." In either of those two positions it needs to be timed. Since I am not familiar with the inner workings of your machine I can't advise you on how to correct timing issues... but if you are a logical, observant and methodical mechanically inclined person, you might see how by really examining the machine. (it may be as simple as loosing a screw or bolt and moving the the shuttle/shuttle race) Take your time and be sure to remember where things go... take pictures if you need to.

Now...Other reasons for breaking of needles are as follows:
Incorrect needle for project. such as sewing denim with a silk or lightweight material needle.

Top tension too tight.

Incorrect threading of the upper threads.

Damaged shuttle or needle plates.

The presser foot improperly installed or wrong foot completely.

Needle positioned incorrectly for presser foot.

Good luck.