Hi,
We have seen this issue before. Shared hosting has spikes and lulls in performance. You are literally sharing a single server with hundreds, if not thousands of other users. During various peak times, you will see degradation in the performance of your shared server. Ultimately, the symptoms are there and you will continue to experience the issue in the long run.
Things like a CDN and caching can help. However, these are band-aids. Shared hosting is designed for small sites, usually static content, with limited traffic. Once asked, your server host should admit that you cannot dependably run a heavily trafficked site, with lots of dynamic content, on shared hosting. You definitely cannot run a secure SSL website like we do here at BeProSoftware.com. Nowadays, we even see, godaddy, bluehost and other major hosting providers offering “wordpress” specific options. These wordpress hosting options typically end up on a VPS.
At some point, you will have to upgrade to dependably deliver continuously low page load times. The decision of when to upgrade depends on your, website popularity, tolerance of the server situation and budget.
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BePro Software Team