Outlook 2013 Memory increase

Question

How do you increase the memory capacity for the Outlook programme on a PC?

Emails are failing to be received. The Outlook send / sent icon hangs there with syncing shown but failing to complete. The emails are on my Web Mail which has unlimited capacity. My email provider has checked and my account and verified it does have unlimited capacity and advice the problem is with Outlook itself.

To fix the problem all large file emails and attachment's have been deleted; Outlook auto archives regularly; all COM Add ins are turned off; etc. In the short term this has fixed the problem but it has now become a daily exercise to go through all emails deleting emails and attachments larger than 1MB and then having to turn off and on Outlook every 3 to 4 hours. Obviously this is a short term fix and even then I foresee this not working soon. Do you have any other suggestions?

As a business I need to keep records of all email correspondence for at least 6 years. So I can't simply delete all emails older than 6 or 12 months.

Is there a way of increasing the memory capacity of Outlook? Would this resolve the problem?

Any other suggestions welcome.