I have been using Duet and a Wacom with my MacBook Pro Retina (2012) for a year and have been very pleased with it.
Last week I got a new MacBook Pro (2015). I've been using the Wacom with it with no trouble. Today I connected my iPad 2 as a second display and it started chiming every second just like you said. As if it's not getting enough power (even though System Information says it is getting 1000mA when only 500mA is required, and there is 500mA extra available).
So now Duet can't run with the iPad chiming because it is constantly disconnecting. I tried various cables, but everything works on the old MacBook just not on the new one.
So I've reset the PRAM and the SMC. I tried charging the iPad to 100% before connecting, with the Magsafe charger connected and without, switching USB ports, disconnecting the Wacom, etc.
Most of the time it just chimes, occasionally it stays connected and charging, at which point Duet will work. Then after a while it disconnects and I can only get it to chime again.
This does not occur with the other MacBook Pro, which is running the same Mac OS (10.11.6) and the same version of Duet (I tried downgrading, it worked once and then no more).
Does anyone know how I might diagnose this as a hardware problem, before I bring it in for service?