This has been happening to my S4 for the last couple of weeks. I've chatted with customer support about it twice (about 1.5 weeks apart). The steps suggested each time were take the cover off, take the SIM out, put the SIM back in. Of course, it works once it powers back up (because that is essentially the same as a reboot) but then after several more hours, it loses mobile connection again, says "Searching" until I reboot it once more.
I'm in the Austin, TX market area and normally get very good reception (3-4 bars).
Is my phone a dud?
Is my SIM a dud?
Is my service a dud?
Do yaks need shaving?