...even when their projects are falling apart. They're so relentless, there's no time for a spell check.
My guess is that the idea this business wants to convey is that the material product of their construction is persistent. But persistence refers to an ongoing process or activity or event, as in persistent fever or persistent inflation. You wouldn't call a wall or a cathedral persistent (except maybe in poetry). Sturdy Construction would be a more appropriate name.
The inadvertent misuse or misunderstanding of language can be funny. My wife and I were driving through Canada with our daughter one time and we stopped to eat near Niagara Falls. My daughter wanted to order a cheeseburger but she wanted it with American cheese not Cheddar which was offered on the menu. When I asked the waitress for a cheeseburger with American cheese she replied that she couldn't be sure where the cheese came from. Consider what the waitress may have been thinking - These arrogant Americans are so jingoistic they refuse to eat cheese made in another country. They demand U.S. made cheese.
I suppose I should've asked for processed cheese.