How tough are strawberries?

I need to up the level of soil in my raised strawberry bed as it has dropped by about 5" despite adding manure/ compost. I think I had bad mildew last year because the plants weren't getting adequate ventilation as they were so low.
Question is.....I don't want to remove all the plants and replant so can I just spread a load of topsoil OVER the plants?
Will they grow up through?

It is best to replace strawberry plants about every 3 years.  So re-fill then.

They've got another year so I'm going to dig them up and transfer to a wider, filled up bed so they can have more air circulating.
I lost alot of fruit last year from mildew so anything to try and solve it!

I'm hoping they are really tough. We had a break in of sheep in our veg patch, they chewed all the green tops off my fantastic 1yr old strawb bed, pulling some out completely.
They pruned all the tips off my blueberry bushes, they even nibbled the first new shoots of my rhubarb (hope it make their tummys sick)

Fingers crossed for my strawbs.