Several things can help. Fill and freeze. Bake off the day needed as close to serving time as possible.. Be sure to bake long enough to get it crispy initially.
Do not cover. If adding a syrup, as in Baklava, use the syrup hot if the product is cold. Conversely, add a cold syrup to a hot product.
Especially, do not refrigerate. How to you prep the phyllo? Do you use the book method? What do you use between the leaves?
if you are using a stretched strudel dough, my one recommendation is when you brush with butter sprinkle some panko bread crumbs (you can season them with cinnamon, etc if you like) before you fill.
Like Helen mentioned, I would freeze and bake when needed. We often made smaller strudels and froze them, pulling them and baking them off before service.
Beyond that, I am afraid Strudel is simply one of those items you can not expect hold well. Everything is going to work against the crispy texture from filling, humidity, refrigeration...like Souffle, this is best served immediately. You have a slightly more generous window of time and it is not nearly as temperamental (once you get through the stretching process), but it does have a limited shelf life once it has been baked. I wish there was a trick I could share, but so far, I haven't found a way to delay the inevitable here :)
I also agree with Helen about freezing and baking. This is what we have been doing for years now and so far it has been working for us.