iTunes and XCode not recognising devices after disconnected, until restart

I have a problem which requires I regularly restart my iMac, up to several times a day, to get devices recognised.

When I re-connect a device, iPhone, iPad or iPod, I regularly get the message:

iTunes could not connect to this iPhone. This device is no longer connected.

They no longer show up as active devices in XCode.

When I plug a phone in, it asks me to confirm it should Trust this computer but that doesn't make any difference.

Note that this is on re-connection. The devices are fine up until the point when I disconnect them. That doesn't change whether I "eject" them from iTunes or not.

Modal nature of problem

It seems that after this problem has started occurring, plugging any new devices in suffers a similar problem.

The problem survived a system restore from backup, which returned some 50GB of space to me. It originally showed up in Mavericks and I have since done an in-place upgrade to Yosemite. It's a [mid-2011 iMac 21.5"][1] with four USB ports.

The problem occurs regardless of whether the devices are connected directly into a USB port on the iMac or via the keyboard's extra ports. The devices are all getting power and show up on the System Report as being connected, eg:

USB2.0 Hub:

  Product ID:   0x0608
  Vendor ID:    0x05e3  (Genesys Logic, Inc.)
  Version:  77.60
  Speed:    Up to 480 Mb/sec
  Location ID:  0xfd140000 / 6
  Current Available (mA):   500
  Current Required (mA):    100

iPhone:

  Product ID:   0x12a8
  Vendor ID:    0x05ac  (Apple Inc.)
  Version:  7.01
  Serial Number:    52c05c8223d3efc793f2815e9d3dbcc018805880
  Speed:    Up to 480 Mb/sec
  Manufacturer: Apple Inc.
  Location ID:  0xfd143000 / 10
  Current Available (mA):   500
  Current Required (mA):    500