Convergence

Theres two parts to the convergence IC's, as after all all they are ar analog stereo audio amplifiers. One or both of one sides of the ICs are bad and probaly blew the fuseable resistors along with the IC's. This is not a consumer repair. theres soldering i9nvolved as well as alighnment after the ICs are replaced. Not to mention the Hi Voltage inside these sets. Please refure this repair to an experienced repair person. Good Luck

If the convergence adjustment is not moving the beam chances are the convergence IC(s) are defective. If you know how to solder and understand TV safety you may be able to fix it. With power disconnected remove the back. You should see two large heat sinks with large ICs (3 by 6 inches) with about 30 leads going through the circuit board. Numbers on the ICs should usually be something like STKxxx-xxx or some variation with x being a number. These ICs control the position of the three beams. If they go bad you can't adjust one or more beams. Replace them both as you don't want to get in there again in 3 months. Cost is not that much. http://www.tritronicsinc.com or http://www.partstore.com should have them at a reasonable price. Before replaceing the ICs look at the circuit board closly for cracked solder joints. Resoldering any bad joints might just solve your problems and avoid replacing the ICs. Good luck and remember safety.

In most Projection TVs including mine, you have to press a specific key on remote or TV to save convergence settings. Simply exiting menu will not save the values you chose during adjustments.
In case of Sharp 55R-WP4H it is preference D you press to save convergence settings. Please refer to user manual for your TV. This could be your problem.

you must press the add button to save the setting of a manual convergence

After adjusting convergence on Sony, I believe you press mute then enter to save the configuration or write to memory.

I do have the schematics for the Apex GB5108 if you would like, email me and I will email them to you