One word I can think of is "bear". Any other words for it? I hate the idea of repeating the same word again and again. I want to use it for trivial things which make your life inconvenient but not hell.
I particularly like deal with, proposed by @MDMcDMD. Here's a way to use it:
My mother-in-law has her arthritis to deal with.
We all have our troubles
is a nice way of complaining.
Here's a nice made-up noun my German spouse invented once:
... the tougheties of life
How about overcome challenges?
"Withstand" or just "stand" : "She withstood the loss..."
endure (that reminds me of a Revenge episode :))
agonise (not really softer)
sustain (as in sustain an injury)
I don't know if the one you are looking for is in this list.