I'd say that it's OK to allow the reposted question to continue, provided that the author is making some effort to get an answer to the question, and isn't repeatedly reposting the same question again and again.
Per the help center page on the Roomba, the main intent of the script is primarily just to clean up the site and reduce the annoyance to other users searching for solutions:
Abandoned, unanswered questions can be a nuisance for readers when they appear in search results. While every question deserves a chance to be answered, at some point the annoyance to those searching for a solution outweighs the increasingly-small chance that an answer will be provided.
The help center page also links to this answer from Shog:
Monica's advice on fixing the
is solid - anything you can do to correct whatever caused it to not
get the necessary attention the first time around is worth doing.
In particular, take this opportunity to add what you've learned in
the time since you first asked.
But then... Just re-ask the question. Sure you can vote to
undelete it, or flag it for moderator attention, or bring it up on
meta... But all of that requires a lot more time and effort - yours
and others' - to accomplish the same thing that re-asking it would.
And re-asking means everything starts fresh. You don't have to
familiarize yourself with the myriad rules for automatic deletion that
might kick in again, or drag along the increasingly-irrelevant history
of the question as it existed prior to its deletion.
So basically, as long as the question isn't being repeatedly reposted, the question is on-topic for the site, and the author is making a clear attempt to honestly get an answer to their question (e.g. by editing it with their own research, by putting bounties on it, etc.), I'd say that it's OK for an author to repost a question that ended up not receiving any attention beyond a single downvote (or instance of Tim Post losing his keys).
Personally, I have a lot of bones to pick with the system categorically deleting all negatively-scored questions without any consideration for anything else, as it has a lot of edge cases, such as if the author is actively improving the question or if it's on a meta site and the only reason for downvotes is because people disagree with the post. But that's for another time.