As with any device filled with micro-electronics, I doubt Roland actually repairs it, in the way electronics from decades ago could be repaired by replacing some failed components.
Yes, there is little that can be easily debugged and repaired in many electronic devices today due to custom logic/control chips and nearly microscopic wave-soldered components although manufacturers may have diagnostic devices to pinpoint common failures.
However, that said I have fixed a number of devices over the years with some simple techniques. One is using the eyes and nose to pinpoint burned discrete components (for those devices that have discrete components!) A burned component is rare, though, and not likely for something that works some of the time and fails others. What I’ve found more likely with symptoms as described by the OP, works for a while then again after a rest, possibly to cool down, is a heat-related failure but not always in a component but in a solder joint on the circuit board. What is sometimes called a “cold” solder joint can fail due to changes in resistance during the use/rest cycles. A suspect connection will sometimes look odd under magnification with a good light, perhaps less shiny. It may heat and cool and change resistance during use, working sometimes and not others.
I’ve fixed many of these over the years in things ranging from complex audio devices to simple auto air conditioner control circuits. The last “tricky” fix was to one of my $1000 Kurzweil synthesizers, intermittent to the point of being unusable. A thermal camera, small heat gun and a can of freeze spray can be a big help. A careful examination showed a potential cold solder connection - the fix was trivial, just touched the connection briefly with a hot soldering tip to remelt the solder. The box worked flawlessly ever since.
Granted, this is unlikely in a wave soldered board with custom ICs and micro components. For those about I can do is measure and trace the power supply voltages, especially checking any connectors and any custom ICs in sockets (increasingly rare these days.) Sometimes faults can be found by tracing with an oscilloscope, especially if the mfgr has provided schematics. And an electronics geek friend can be a huge asset!
I would at least try the freeze spray - when it won’t start, try cooling various sections, one at a time, and see cooling some spot causes it to start.
Or just send it back and let them replace the boards!
JKJ