When watching our Toshiba 50H71 it just turns off then back on.

Click here to download the manual.

Remove the lower speaker panel. Then you will see a series of screws along the bottom edge of the screen frame. remove those screws and then grasp the screen frame and slide it up slightly to disengage the upper clips then lift the screen assembly away enough to unplug the wire and then the screens can be accessed.

The convergence needs to be repaired. The 50H71 convergence kit works in your model as well. You can get the kit at the following link which contains the parts and instructions.
http://servicemanuals.vstore.ca/product_info.php/pName/toshiba-50h71--50h81-convergence-repair-kit/cName/convergence-repair-kits

How To Enter Service Menu is what you need to know and replace both of your STKs these ic chips control convergence.If they are STK392-110s use STK392-180s better ics.

you need to replace both the convergence ICs they are STK392-110 you can get new replacement ICs at the following link and they will provide free instalation instructions with pictures so you can do the repair yourself. Heres the link.
http://servicemanuals.vstore.ca/

try to turn down the screen control and see how the tv reacts.

set most likely has bad convergence ics J.D.W.

It may be solder related, but it may be something such as aleaky diode causing secondary voltages to increase thereby shutting down your set for protective measures. I would recomend getting a service manual and some free support to help you diagnose this. You can get both at the following link.
http://servicemanuals.vstore.ca/

What happen lost you?

This is like so many sets I have seen here. This problem has to do with the shutdown circuit turning the set off to protect it. As has been said many times this is a problem with the HV section which inclused the deflection, convergence, and horizontal output. These sections can not be repaired by someone who does not have electronics experience. I would suggest that you take this telvision to a repair shop in your area.