What is the suggested edit queue size limit?
When an edit is suggested to a post, it needs to be reviewed by members of the site's community with editing privileges. This takes place in the Suggested edits review queue - for more information, see How do suggested edits work?.
In order to ensure that edit suggestions are reviewed in a timely manner and to prevent the site from being overrun with more suggested edits than available reviewers, each site has a maximum number of suggested edits that can be pending at any given time. Once the limit is reached (i.e., the queue has reached maximum capacity), no more suggested edits will be accepted from anyone until some pending edits get reviewed.
What happens when the queue is full?
If the queue is currently full, the system will produce an error message telling you that you can't currently submit a suggested edit. You will only get this error if you try to edit before you can access the editing form. (If you were able to open the editing form before the queue filled up, you will be allowed to submit your edit even if the queue is full.)
We recommend trying again in a bit, once reviewers have had a chance to review the existing suggested edits in the queue. On large sites, it will generally take only a few minutes for some other edits to get reviewed. On smaller sites, if the queue is still full after several hours, make a post on the site's per-site meta or post in the site's chat room encouraging the site's community to review pending edits.
How large can the queue get?
The maximum size of the suggested edit queue is set to 40 by default across the Stack Exchange network, but Stack Exchange staff can configure it to be larger or smaller on a per-site basis.
Currently, these are the exceptions to this default:
Are there other reasons why I may not be able to suggest edits?
The edit queue being full is only one of many reasons you may be blocked from suggesting edits. Note that in addition to the site-wide limit described here, there is a limit of how many suggested edits an individual user can have pending at any given time (5 on most sites, 20 on beta sites).
This and other potential reasons are listed at Why is the edit button disabled?.
Can a site change the size of the queue, and if so, how?
The limit can only be modified by Stack Exchange employees, but you can request for it to be changed on the site's per-site meta.
Keep in mind that the intent of having a limited size is to ensure that edits are reviewed quickly and prevent the site from being overrun with more suggested edits than available reviewers. Simply having the queue limit raised without having more users available to review edit suggestions will mean that the new limit will be reached, negating the change. A good case for increasing the queue size is if the site has a high population of active reviewers but the queue is routinely full because of a high volume of editors.
Once you have a good case for increasing the queue size, start a discussion on your site's corresponding meta site explaining your case. Allow time for the community to discuss your arguments and determine if a change is actually appropriate for your site.
Once it looks like it has a positive consensus, escalate it to Stack Exchange staff by tagging it with status-review if you are a moderator, or flagging it for moderator attention requesting for the tag to be added if you're not. This will raise the post to the attention of Community Management, who will take a look as soon as time allows.