Karolina Protsenko, the famous young violinist, said she keeps her violin with her at all times ever since someone broke into her parents' SUV. Luckily they didn't take or damage her violin, but they did get away with multiple electronics and microphones and stuff.
I work for a lighting and staging company and it's different with each artist, some we hold on to for the artists, some are donated to us, most are kept on the tour trucks with the crew chiefs keeping eyes on them all the time
I'm no famous musician, but I am a player and have a lot of friends in the business - both big and small. Some have studios and secure buildings. Many, if not most, keep their babies close. I know that I do.
The bigger the artist, the more likely they are to have a crew handling their gear. It is probably in whatever trailer or van they use to transport the gear when not on stage, then on/around the stage pretty quickly once the artist gets to the next city.
The only reason Tom Petty was in the Wilburys was that George Harrison left his guitar in Petty's studio, and had to go get it. He brought Petty back with him.