I would like to know if there is a maximum number of downvotes a question can receive, or if once downvotes hit a certain number further downvotes are blocked.
There is effectively no hard limit, but it's probably not useful to have one.
The system does not attempt to impose any particular limit on how low a post's score can go. It probably cannot go lower than -2,147,483,648. But in practice, it is extremely unlikely that any post will ever receive billions of downvotes! The number of users on the site who have enough reputation to cast downvotes is an approximate limit on the lowest possible post score, though there are also some limited situations where the system casts a downvote automatically.
Here on meta, and on community wiki posts either here or on the main site, downvoting does not decrease the reputation of either the post author or the voter. However, for non-CW posts on the main site, downvoting an answer costs the voter 1 reputation. Users with less than 125 reputation cannot cast downvotes, so there is already a mechanism in place that limits how many downvotes people are able to cast as well as how willing people are to cast them. It is much easier for an answer's score to increase to an unexpectedly high value than to decrease to an unexpectedly low one.
But what about downvotes on questions?
Zanna has pointed out a major gap in my (original) reasoning here. As she had commented: "Downvoting answers costs 1 reputation point, but downvoting questions is free." Therefore, this mechanism does not limit the number of downvotes cast on a question! I think that in practice, extremely downvoted questions on the main site will remain rare (or nonexistent), but I cannot be sure of this.
- For the most part, people don't vote nearly enough on questions, up or down, so if this did become a problem, then it would probably come as the downside to an overall excellent change in the culture of our site.
- Typically, a question that contains enough information to answer won't garner thousands, or even hundreds, of downvotes. It's hard for an answerable question to be bad enough for that. If it did happen on an open, answered question, some users would likely cast upvotes out of sympathy. This is looked down upon, but it does happen, and in such an extreme situation there might be an argument for it. For a closed question, the question would likely be deleted before its score got extremely negative, since 3 delete votes from 10k rep users will delete a closed question.
- However, sometimes a really bad, confusing, poorly researched question gets spectacular answers, yet people cannot agree on how to improve the question. If the question does not qualify for closure, it will stick around even if its author would otherwise have deleted it (the system will prevent them from doing so) and it may continue to garner downvotes for all time. Even then, some users will presumably upvote it, with the view that it has proved its value.
- A question could potentially garner many downvotes based not on its quality or the depth of research that went into it, but due to disagreement with what the OP is trying to do. On the main site, it's pretty strongly discouraged to use downvotes to express disagreement. But it does happen, partly because the lines between what one opposes and what one thinks reflects inadequate research and consideration are subjective. However, I think such questions are unlikely to drop extremely low in score unless they have (other) problems. Some users will upvote them for their technical merits. Others will upvote them to express approval ("Censoring access to information about multiplication on the school library computers you manage? Awesome!") even though they really shouldn't do that either.
So I do not advocate a lower limit on question score, either.
I expect we won't ever get either lower or upper limits on post score.
The Stack Exchange system (which Ask Ubuntu is part of) is changed from time to time. So it is possible that Stack Exchange developers will add a limit in the future. However, I don't see why they would. If they were going to impose a limit, it would probably be on how many upvotes a post could receive, because as detailed above, that's the quantity that is more liable to change rapidly and unexpectedly.
I don't think it's necessary to constrain either one. In addition to expecting that no such limit will be imposed, I also hope it won't be.
The related, but different, issue of rep loss.
At least in theory, there is an argument for limiting the rate at which a user can lose rep from having their posts downvoted. In practice, though, I don't think this is necessary.
The amount of reputation increase we can get from upvotes on our posts is capped at 200 per day, which is the amount conferred from 20 upvotes on answers or 40 on questions. To suffer a decrease of 200 rep from downvotes on either questions or answers would require 100 downvotes. This is unlikely to happen to anyone over a short time, especially in a single day.
(You are more likely to lose lots of rep from unupvotes, where a user who upvoted your post later retracts their vote. But mass unupvoting doesn't seem to be common either.)
However, if this started happening to people a lot -- instead of...never? -- then it would be worthwhile to look at why and to consider imposing a limit on how much a user's reputation can decrease in a single day due to downvotes. It would probably still not be useful to impose a per-post downvote limit, though.