No problem leaving it up, I guess. You just will get water and debris underneath it.

I glanced at the Service Manual and it mentions a safety feature built into the spoiler operation. If something impedes it as it is retracting, then it will go back to the full-up position.
Is it possible that it is sensing some dirt or something that is impeding it that is making it go back up?
Just a wild guess. It wouldn't hurt to look very carefully at the mechanism and degrease the parts that move and then re-lubricate them.

Other than that, I would guess it's something electrical.....

Here's a cut-and-paste from my Service Manual copy. I added the underline and bold to the pertinent sentence....

Page 23-311 of Service Manual
2005 ZH Service Manual Publication No. 81-270-05036

To prevent injury, the rear spoiler retracts in defined steps to allow time to pull any hands or foreign objects that may be in the path of the rear spoiler before it is all the way down. If the rear spoiler gets disturbed while retracting automatically or while retracting manually, the rear spoiler is automatically driven up again and will lock in the up position. During manual retraction, if you let up on the switch, the rear spoiler will be driven to its up position. When retracting the rear spoiler manually, a single audible chime is produced to indicate to the driver that the rear spoiler is in the fully retracted position. A warning signal (LED) on the spoiler override switch illuminates, indicating a mal- function to the driver. A malfunction that prevents the spoiler from deploying illuminates a red warning lamp in the override switch.