My apologies to you. This thread was overlooked while some staff was out of the office. We should have responded sooner.
What the support response was saying is that the code of the site is causing a loop. Meaning, there is essentially a near-never-ending request for the page or some element on the page, possibly the effect of each request causing an additional request. Eventually, this causes the user to hit the maximum concurrent connections allowed for the account which is what a 503 error normally indicates.
Often, when we see a 503 error, this is because of legitimate traffic causing the site to hit its max connections. Regarding the upgrade to Deluxe, I assume a representative suggested that to you when they saw the 503 error since, in those legitimate traffic situations, an upgrade would help by raising the limit for the account. However, in your case, it's a coding issue causing an abnormal spike in connections which would hit the limit of a Deluxe account as well. So, for you, upgrading is not the answer. If you don't need the upgrade, you're welcome to downgrade back to the Economy plan. Just let me know, and I'll review the billing ramifications.
Unfortunately, what I can't diagnose is the exact code that's causing the problem. Since you only see it when using the Nimble theme, I must recommend contacting the theme's author for assistance or switching to another theme you find suitable. I apologize that I can't do more to resolve the issue.
Please let me know if there's another area where we could assist or if you choose to perform the downgrade.
Good luck to you,