Leave the Cover Open While Traveling?

[FL Person]

I've had this tub for about five years (2016 Bullfrog R6).  For the past two years, it's been empty and unused.  I emptied it while some construction was being done at the house and never found the motivation to refill it.

I travel for a living and I'm routinely gone for one to two weeks or more at a time.  Since I've had the tub, with the cover closed for two weeks straight (or longer), mold and mildew began to grow on the underside.  It got to the point where the mold/mildew must have gotten into the foam core of the cover because it would reappear fairly quickly after a thorough cleaning.  It got so bad, I replaced the cover when it was just a bit more than two years old.  The tub is under-roof on a lanai in FL, so it was still in excellent shape, other than the gross mold/mildew.

Now that I've refilled the tub, I'd really like to mitigate the same mold/mildew growth issue but my frequent travel will remain until I retire in ten years.  I'm wondering if I should/could simply leave the cover open while I'm away for a week or more?  I can lower the preset temp while I'm away but I keep the tub in "rest" mode, so it's only heating for the three hours that it filters each day.

Thoughts?  Things I'm not considering?

Thanks.

[A.O.]

My only concern would be stuff falling in..

[FL Person]

My only concern would be stuff falling in..

The tub is underroof in a screened enclosure (lanai).  There's nothing to fall in but dust.

Any additional thoughts?  I'm inclined to leave the top open the next time I leave town.

[FL Person]

I was gone three weeks and left the cover open.  It was nice to come home to clean, clear water and a dry cover without a spec mildew or mold. 

But wow!  I was really surprised how much water evaporated in three weeks.  I'd guess roughly 6"-8"!  The level was at the middle point of the highest jets in the tub.

One problem averted.  Another problem created.