Lego Arms and Bath Boats

I am amazed at how losing the arm of a microscopic lego man can be so detrimental to a five year old boy. I am equally amazed at how long it takes him to get over this loss. His little world is disintegrating before him faster and faster the longer it takes him to find the missing appendage. I swear we've looked in every possible nook and cranny of our not-so-huge house and the arm has yet to raise a hand to it's wherabouts (hehe). My question is, how long is the appropriate length of time to look for something like a lego arm before you have the go-ahead (sans guilt, if it's possible) to stop looking and call it a loss?

The other day Carter lost his new boat he got for in the bathtub. I spent exactly 38 minutes looking for that boat before I found it. That's a long time when you've got 2 other kids, a dog, dinner and dishes to take care of. But I spent the time, I found it, and I was a hero. For about 5 minutes. Then he moved on to another toy. An old toy, nonetheless. I spent the next 38 minutes wondering if it had been worth it in the first place beings that the fun he had with it lasted a fraction of the time it took me to find it. Aaaaahhhhh, the joys of rhetorical questions. I doubt I will ever know the answer, as I have yet to recieve solid answers to most of my parenting questions thus leaving me in the dark (with a minimal amount of confidence) while making them. I am however, learning throughout the process and I have no doubt that I will be a parenting guru by the time my kids are grown and start having their own kids... and I'm sure my grown children will have grateful smiles on their faces as I (ever so humbly) dole out the parenting advice as they are enjoying the wonders of parenting as I did. Right?