Depending on the model of the UPS, you might be able to get some information from the monitoring software that comes with it. Connect the USB cable that came with the UPS and install the software. Usually there will be a log inside the UPS that it can read that will show you when and why it failed. Contact the manufacturer and see if they have any suggestions.
My suspicion is that the UPS isn't switching fast enough for the computer.
A line-interactive UPS handles brownouts without relying on the battery by using an adjustable transformer - the transformer adjusts the incoming voltage to the proper 110 or 220V that you normally get. However, while it is adjusting you lose power for a few milliseconds. This rating is probably NOT the same as the transfer time (where it switches to battery). Usually it's less than 10ms, but it could be that yours is slower or simply defective.
In most cases, it switches fast enough that the connected devices don't notice. Power supplies usually have big enough capacitors in them to run for a few milliseconds after they lose power. But if you have a weak or cheaply made power supply in your computer, it may not be able to handle it.
I can't think of any way to test this except to wait for the next brownout. Plug something like an LED light in and see if it turns off for a noticeable amount of time, longer than the time it goes off when switching to battery. If so, we found the problem.
If it is a defect, the manufacturer should replace it for you free of charge. If not, I'd recommend either replacing the power supply in the computer (if it is old, cheap, or underpowered for the system it's in), or getting a better UPS.
If you live somewhere with a lot of power issues, you may even need an online UPS, where it is constantly converting the AC power from the wall to DC and charging the battery, and converting it back to AC to power the computer. An online UPS doesn't have a switching time at all, and won't cause the computer to reboot.