They should be fine. I was worried about the same thing, but since we've actually had a few days with no rain, those pots dry up quickly. We had 4" in 4 days last week, and over 7" in June. Many of my pots are already in need of watering and it just quit raining on Saturday.

As long as your soil is well-draining and your container not over-sized with respect to the palm, I wouldn't worry--especially if temps have been warm to hot. Keep in mind that while Washingtonias do thrive in hot, arid regions while growing in the ground) their deep roots manage to make contact with sources of ground water--which they can't really do in a container but attempt to. If you've ever had the experience of having a Washingtonia or Phoenix deeply rooting itself into ground through the drainage holes after a summer outdoors you'll understand. Similar to date palms in the desert, while the fronds are baking in the sun, the roots have an adequate source of moisture. So they aren't as arid loving as you may think (compared to cacti or succulents). Heavy, wet soils are a different question and here palms from Mediterranean or desert climates may be particularly vulnerable to excessive moisture at the roots (Washingtonia, Chamaerops, many varieties of Phoenix). Hope the sun comes out soon!:)

Thank you both for the help and info! This is my first year growing Robustas and I don't want to make a mistake if I can help it. :) BTW, the sun IS out today and the forcast looks good for the next couple of days!

My Wash. Robusta does not grow much, it stopped growing completely. It's all very confusing when some say it needs to stay dry, some say water the entire plant and some say it loves plenty of water! Take a look at this article (click the link below):

Here's an excerpt from it:

http://www.florida-palm-trees.com/mexican-fan-palm-tree/

"It can also tolerate drought but grows much faster when receiving plenty of water."

Here is a link that might be useful: Plenty of water or plenty of dry?

Most palms require excellent soil drainage but most are also only moderately drought tolerant. All those desert palms (Washingtonia and Phoenix for example), may have their tops in the hot, arid sun but they send down deep roots to tap into subsurface aquifers. Growing my Washingtonia in large containers, I water them every day in the grow season as our summers are hot and they get full sun all day.--They respond with rapid growth. If your Washingtonia has stopped growing, you need to consider the following:

i.) Is the container big enough?
ii.) Are you fertilizing?
iii.) Are you watering enough?
iv.) Is your palm getting enough sun and heat?

PS., I referred to your article and as the above suggests, they like moist but well-drained conditions--there is no contradiction here. Good luck!