Intuitively, I'd expect this to matter somewhat, all else being equal -- but all else is rarely equal.

In the nonprofit world, a promising organization might succeed or fail based on the amount it can raise within a few months. These org-specific timing considerations will, I suspect, usually overwhelm macroeconomic considerations. If you decide to wait until an economic slowdown, and it takes two years, you might see a dozen promising organizations emerge or fade away in the process. Heck, if you had decided in 2009 to wait until the next recession to give, you'd have missed... essentially the entirety of the EA movement.

At this point, with a recession being more likely to happen within a few years than was the case in 2009 (maybe?), it could make sense to save money. But I don't know how much EA giving lines up with economic cycles, for a few reasons:

• A lot of donated EA money comes from very wealthy donors who have already set aside tens or hundreds of millions of dollars in safe places that a recession won't impact much
• Another good chunk of EA money comes from people who made a pledge to donate a fixed percentage of their income, rather than seeing charity as one of the first things to cut back on when times are tough (as I'd guess is the case for many donors outside of EA)
• A lot of people in the EA community have jobs that are fairly "recession-proof". They tend to be highly educated and work in growing sectors (as opposed to, say, construction)

All in all, I'm moderately confident that EA giving during a recession would drop much less than the general public's giving, though we aren't wholly immune to the larger economy.

I suspect much of the trouble is the same as the trouble investors have trying to take advantage of this strategy: it requires marking a better prediction than the prediction the market is implicitly making with its current prices. Although it seems reasonable to predict that a recession will come "soon" since it's been unusually long since the last one and they appear cyclically (approximately coordinated with the approximately 5-year business cycle?), making that prediction too soon and switching to hoarding assets in anticipation of a drop so you can re-buy assets when they are at the bottom to maximize gains on the way back up will result in unnecessarily giving up potential gains. You might make a lucky guess once, but in the long run you'd need some reason to believe you can predict recessions or else you will perform worse than the market, not better.

So this seems probably only relevant if you are so good at predicting recessions so you can use that to make money and then donate that money, and will probably also require keeping quiet about your prediction and your evidence such that you can maximize the amount of advantage you can take (up to the limit of your funds, including the use of leverage, which might cause you to carefully share your knowledge in an attempt to fill gaps in opportunity you wouldn't be able to take advantage of yourself). If you're a non-profit, regular donor, or anyone else, you're probably best off not trying to beat the market, and only accounting for this in the normal way of holding funds in reserve so you can weather temporarily shocks to the market, i.e. have enough operating capital that you won't have to draw down on your investments before they recover.