I have only used the side burner once, and left it on hight the entire time to saute some asparagus so I hadn't experienced the problem you did. I tested the side burner this evening and found that you are correct, the burner has two modes, high, and medium high. I could not turn the burner down very low at all which is a little bit disappointing to find out.

I hope that you will contact Virco and ask what's wrong. I plan on doing so. Hopefully other Virco owners can confirm whether this is normal operation, and whether they have found a solution.

I believe this is done on purpose as I had discovered the same issue with mine when I was on LP. A good friend of mine has a Weber Silver C Series with a side burner and it does the same thing. I think the intention was that if the burner was allowed to run too low, it might blow out. Since the grill comes as an "LP" model, the gas is heavier than air. If the burner was to blow out easily, the gas could build up somewhere lower than the burner and then it could migrate to the mains if they were on. The next thing that could happen is obvious. When I converted to natural gas, I found the low on my side burner to be much better. Of course, natural gas being lighter than air, if it blows out, the gas just dissipates upwards. I don't know if that is a lot better, but at least I know I won't get an explosion.
A couple of things you could consider, one would be to convert the grill to natural gas. The other is to make the valve smaller. The way to do this is to first remove the front cover of the grill by removing all of the knobs, then the screws holding each valve to the cover. Next, remove the four screws holding the panel on (two on each end) then you can pull the front panel forward, exposing the wires attached to the igniters. Once you gently pull the wires from the igniter modules, the front cover is free to be removed. Now, you can disassemble the front of the valve for the side burner with two small screws then remove the stem and front of the valve. When you do this, be careful not to lose the spring or "D" ring when you remove the stem. Once this is out, you can remove the brass cone inside the valve, it simply pulls out. If you use needle nose pliers to do this and to hold the cone, this will keep the grease on the cone for smooth turning. If you look at the cone, you will notice a small hole and a large hole. The large one is for the high setting and when the valve is in this position it allows the flow of gas to be controlled by the orifice. When the valve is turned to the small hole, this hole size controls the low setting. I did this successfully on my friends Weber and it worked out nicely. Once you have located the small hole, you have to make it smaller. The only way I have seen this accomplished without replacing the cone, is to solder the small hole shut, and then re-drill it to a smaller size. You will need a numbered drill bit set for this project and (Of course) you will want to turn your gas off first and disconnect and remove the tank just to be safe. I have included a link below, which will show you pictures of what a similar gas valve looks like apart. It is from a Members Mark, but the internal portion of the valve is identical. I would recommend probably starting with a #70 and trying that first. If it blows out too easily then increase it (lower drill number) one size at a time. A #70 should yield about 5500 BTU's with 11" of LP. I am running a #60 on my low setting which yields about 5750 BTU's at 7" of NG, so this should be fairly accurate. I hope this helps and there is also a chart to show you these BTU figures at the link below. Good luck.

Here is a link that might be useful: BTU charts and valve pics

Yes, I noticed the same thing, and I concur that the reason is probably for safety against the flame blowing out.

After the initial test of the burner, I really haven't used it for much. I figure it might be useful for making typical BBQ fare like corn-on-the-cob, or maybe steamed veggies. Mostly I keep the burner cover closed and use that area to set things, as the space where the Virco is set is tight and I haven't attached the side shelf.

One way to get less heat is push the control knob in and turn toward off..just make sure the flame is still there and I would not leave unattended for lengthy periods. I do this with the main controls to get a really low heat for slower cooking.