Hi Rosa,
I’m sorry to hear that you’re facing some difficulties.
When you try to load the next month’s events (in that widget) a bad response is coming back, which points to a fatal error:
Allowed memory size of 67108864 bytes exhausted (tried to allocate 77824 bytes) in /.../plugins/backwpup/inc/class-destination-sugarsync.php
Despite what this says it isn’t necessarily the case that you lack sufficient memory, as such, though it is definitely a possibility you should consider and increasing the available memory may help (see here or talk to your hosting provider).
However, the fact it only seems to happen following an ajax request – whether in relation to the calendar widget or month view itself – makes me think we may actually be looking at a conflict of some kind, which has this side effect of depleting the available memory.
Trying our standard troubleshooting steps would therefore also be worthwhile, here (starting with your “backwpup” plugin and perhaps looking at its settings in relation to “sugarsync” may be a great starting point).
Let me know how you get on!