I'm reasonably sure that shower heads are not supposed to fall off when adjusted. In fact, I'm absolutely positive that this is a malfunction suggesting the (somewhat urgent, perhaps) need for replacement of the shower head. And can I make a link to education and teaching? You bet I can.
I will be making a trip to the nearest DIY ('do it yourself' store) to purchase a replacement shower head and, well, do it myself. Despite knowing friends who could, perhaps, do it more quickly and having plumbers in my community who could just do it for me, it would be inconsistent with most everything I write and say to simply turn this over to someone else. Far too many of us in the 'developed' world have lost the ability to do much more than drive to work and use computers to help us analyze and communicate data. Though I hear less of it now than I did in previous circumstances, I cringe when I hear 'outsource' used in conjunction with household maintenance, activities of daily living (cooking, for example), and the raising of our children.
The single act of replacing the shower head (which has, in case you're wondering, cracked at the juncture where the threaded section attaches) won't change the world or make much of a difference. But embracing the mindset that capable people make better citizens--which includes better parents, better teachers, better employees, and just better people--and practicing that mindset to the fullest extent possible may make me a better parent, teacher, and friend.
Thoreau would have approved, I think.