You have plenty of storage left on your plan, last month you checked bandwidth usage and it was nowhere near the limit, and yet the site occasionally throws a strange error when several visitors arrive at once. If storage is not the problem and total traffic is not either, what is probably running out is something else: the simultaneous process limit.
What a process is, in plain terms
Every time someone visits a page on your site, the server has to run code to build that page: query the database, run the plugins, generate the HTML. That execution occupies a process for as long as it lasts, usually a fraction of a second, but during that instant the process is active and counted.
On shared hosting, each account has a cap on how many of those processes it can have running at the same time. It is a different limit from disk space and from monthly bandwidth: it measures concurrency, not accumulated volume.
The symptom that gives this away
It is fairly distinctive once you know what to look for. The site works fine most of the time. But when several visits land at exactly the same moment (a traffic spike, a search engine bot crawling the site in parallel with real visitors, or several forms being submitted at once), you get a server-busy error or a blank page outright, which recovers on its own after a few seconds.
The key is "at exactly the same moment". A site with a thousand visits spread across the day has no problem. The same site with fifty visits concentrated into the same minute can hit the limit, even though the day's total is perfectly reasonable for the plan.
Why it is not the same as "low total traffic"
This is what confuses people most. Statistics panels usually show total visits, bandwidth consumed and storage used, and all those numbers can look calm while the process limit gets hit every day at the same hour. They measure different things: one measures how much overall, the other measures how many at the same instant.
That is why, when the error always shows up at the same time slot (the busiest hour of the day, or right after publishing something that drives a spike), it is almost always this limit rather than a storage or accumulated-traffic problem.
What makes it worse
Some causes multiply process consumption without real traffic having changed at all.
Heavy or badly written plugins. Every visit that triggers several plugins at once consumes more processes than a visit to a light page. A plugin running slow queries keeps its process active longer, which raises the odds of several overlapping at once.
Aggressive search crawlers. Search engine crawlers sometimes sweep many pages in parallel. Combined with real visitors at that moment, it can push the total past the limit.
Missing cache. Without a cached page, every visit runs the full generation process. With a cache, most visits are served without touching that allowance at all, because nothing needs to run: a ready-made copy is delivered instead.
How to fix it, in order
1. Set up a page cache. This is the single biggest improvement. By serving already-built versions for most visits, it drastically cuts how many real processes fire per minute.
2. Check which plugins consume the most. If you can measure execution times, you will find one or two taking far longer than the rest. Replacing or removing them, if unused, frees up headroom.
3. Throttle aggressive crawling if needed. You can ask bots to space out their visits through each search engine's own administration tools, without losing indexation.
4. If the site has genuinely grown, talk to support. Sometimes the plan's limit is simply too small for what the project has become, and the direct fix is moving to a plan with more headroom or to semi-dedicated, which allocates resources with far less crowding.
Why it is worth understanding this before changing plans
The most common mistake is assuming more disk space is needed when the real problem is concurrency, and ending up paying for something that fixes nothing. Before upgrading over this symptom, it is worth optimising cache and plugins first: in most cases that resolves it without overspending, and if the limit still gets hit after that, then upgrading genuinely makes sense.
How to confirm it yourself before writing to support
You do not need to wait for support to confirm this to have a well-founded suspicion. Write down the exact time the error appears the next few times it happens, and compare those times against your busiest hour of the day, based on what your statistics panel shows. If they match, the process-limit hypothesis gets a lot stronger.
Another way to confirm it: if the error disappears as soon as traffic drops, without you having changed anything on the site, that is a further sign the problem is concurrency rather than a one-off bug in the code. With that information in hand, your report to support will be far more precise, and so will the answer you get back.