The 60 flashing could indicate low system pressure or pump failure.
However the sequence you describe of the temperature fluctuating is often caused by a sludged up plate heat exchanger - do a search on the Potterton Performa which is a similar boiler. (The Luna badged version is not sold in the UK AFAIK)
This sounds frighteningly similar to our problem with our Baxi Luna 310.
For the last nine months, our hot water has intermittently cut out in the midst of a shower. The boiler will work great for a while, then once it starts cutting out the hot water, it never gets better. Only worse. Every two minutes, heat cycles down to 50 (and the water gets cold), then something kicks in and re-cycles back to 80. The pressure is about 1.25 bar
We've had technicians here four times, and so far they've adjusted the system pressure and replaced a diaphragm, something behind the shower control and most recently the unit's control board. Each of these "fixes" has lasted for a while, but nothing solves the problem.
I'm particularly peeved this time because the control board ran me almost $400 and fixed the problem for three whole weeks.
Any suggestions?
As an aside, we own a flat in an old shoe assembly plant that was converted in 2004, so everything is new. All 34 units have the exact same Baxi Luna 310, and three-quarters of them (that I know of) have had the same problem despite regularly scheduled maintenance. So if anyone could actually solve the problem, there are at least 25 families who would be eternally grateful.