Don't know what part of the world you're in but in the US there are different places across the country, mostly universities, that conduct turf trials.
Grass isn't just one type of plant. There are many different cultivars of grass. Different cultivars have different characteristics which may be different in different regions. One of the characteristics they test for is traffic wear. How well the grass will hold up over foot traffic.
since grass is used on many playing fields, there is quite a bit of research on "sports turf". There will be blends of seed marketed as sports turf but I personally like to see independent research from the various turf trials around my area. in the US theres also NTEP which helps organize or at least colates the turf trial data.
You should also look for information on how sports turf is managed. There is much written on the subject and you should hopefully be able to find information for your area. You can also try talking to people in your area that manage the grass for sports fields and get their advice.
You can't really protect the grass but you can get grass that will withstand that type of abuse better and spend a little more time taking care of it so it will look good. At least during the parts of the year when it's growing. In the winter, depending on your climate, it's not really growing so can't recover.
A couple of things you'll want to do is aerate the lawn to relive soil compaction and overseed to fill in bare/damaged portions. Depending on how much abuse the lawn gets you may need to overseed and maybe even aerate spring and fall. Also make sure you fertilize according to the type of grass you use so your grass is healthy enough to withstand the abuse.
You may not have the best looking lawn in your neighborhood but with some care it should be better than you describe and your kids will still get to play. What's the point of having a nice lawn if they can't enjoy it anyway. :)