As expected

Noticed this on my GW-9300, after a few seconds of readout it also goes blank. Not sure why, guess perhaps a power saving thing.
As Rutteger mentioned it's power saving function. In addition to the 20 second continuous compass measurement, it also takes temperature readings every 5 seconds. You can do store bearing memory every 20 seconds which allows you to take subsequent compass measurements:
During the 20 seconds that the digital compass measurement is in progress, press (A) to store the current direction angle reading in Bearing Memory:
The Bearing Memory direction angle flashes for about a second as it is stored. After that, the Bearing Memory screen will appear, and a 20-second direction reading operation will start. While the bearing memory screen is displayed, you can press (C) to start a new 20-second direction reading operation, which displays the direction angle for the direction that the 12 o'clock position of the watch is pointed.
Technically you could have a continuous compass display if you use the bearing memory feature and press either (A) or (C) before your seconds are up LOL.
From the 3261 Manual:
Digital Compass
20 seconds continuous measurement; 16 directions; angle value 0 to 359; four direction pointers; calibration (bidirectional, northerly); magnetic declination correction; bearing memory
Thermometer
Measurement timing: every 5 seconds in the digital compass/thermometer mode