I've not had any problems in recent years, using Firefox... but came across a new twist just now:
Received the standard "check in for your flight to the Netherlands and onward connecting flight(s)" email for my flight home tomorrow... but it only showed the first of the two flights (to AMS), not the onward one back to LCY. And when I clicked on the link I had the same thing - only one flight shown.
There have been previous occasions when I have not been able to check in for the second flight, but on those occasions that second flight was always shown, albeit greyed out. This time the system seems to think that I am only booked on one flight which is rather odd.
Will have a look again later (when both flights are within the 30 hour window).