Fatal error: Allowed memory size exhausted

You could try increasing your available memory to 256MB in the wp-config.php file (take a backup copy first):
http://codex.ww.wp.xz.cn/Editing_wpconfig.php#Increasing_memory_allocated_to_PHP

This may or may not work depending on how much memory your host allocates.

You could also install a plugin to check if any of your plugins are using excessive memory:
https://ww.wp.xz.cn/plugins/p3-profiler/faq/
https://ww.wp.xz.cn/plugins/wp-memory-usage/

Apologies. Here is the correct path:

http://codex.ww.wp.xz.cn/Editing_wp-config.php#Increasing_memory_allocated_to_PHP

No problem. Yes that is the correct code to add on a new line in your wp-config.php file – NOT your wp-settings.php file.
Again, create a backup of the file before making any changes.

You can check to see how much memory you are allocated by installing:
https://ww.wp.xz.cn/plugins/wp-memory-usage/

Then, you can delete that and add the p3 profiler plugin to see which plugins are using the most memory. If your host refuses, or is unable to increase your memory allocation, you could explore alternative plugins which have a lower memory requirement.

I would delay getting in touch with your hosts and keep the p3-profiler activated for a day or two. It may be that one of your plugins is idling now, but when it is active it drains your available memory. The average memory usage over 48 hours might show this more clearly. What plugins do you have installed, and do any have a history of being memory hungry? If you have access to your cPanel, then you could also keep an eye on your Resource Usage to see whether your memory peaks coincide with anything you have scheduled such as security scans.

Your memory resources profile doesn’t look too worrying. I’ve now realised that the p3-profiler doesn’t log an average usage over a 24 or 48 hour period, but just the average for each scan you make – so evaluating things over an extended period probably won’t make too much of a difference.

25 plugins could be stretching your memory limit at times when several of the plugins are in action simultaneously. Is there any way you could trim down that number? Duplicate functionality or alternatives that combine several functions in one plugin? Maybe posting a list of the plugins you use here here would be useful, as forum users may be able to offer their opinions. Also, perhaps see if your host will increase your memory to 256 mb, as this would be an easier solution than changing plugins and trialing/setting up new unfamiliar ones ones.

Fantastic news – the easiest solution prevails! In situations like this you can congratulate yourself on choosing a responsive and proactive host. Makes all the difference. Best wishes.