The attachment was uploaded to the computerhope server. It wasn't uploaded elsewhere. Whether Nathan (the admin here) deletes them manually or whether he has a script that runs on a schedule that clear older attachments, the fact is that those attachments use up disk space on his server, not some other server.
Upload the images elsewhere- such as photobucket, or via a webhost. Many ISPs also give you some webspace to use, too. You can then use the forum to either link to those images or insert them in-line. Fore example:
If we return to this thread in a few years, as long as my site is still active, and that picture is still there, the image will appear. It doesn't use any space on ComputerHope; and doesn't reside on the server. The purpose of attachments here would be a short term exchange of files as a person is having their problem solved; the files themselves have little to no value afterwards and they are consuming disk space on Nathan's server. If he had allowed all attachments to stay, who knows how much space they would be using! Instead they have a time limit, or he goes through old threads and removes attachments to preserve disk space.
If the data is important... keep a copy. It's too late now, presumably, but the fact is that forum attachments are not a private storage repository for files, and in order to attach the file you need a copy on your local machine anyway. I prefer to avoid attachments because I have my own webhost anyway and can ensure the image will always appear- unless I do something, or my post is edited. Also, it feels "better" because I'm not using CH server bandwidth, but rather my own. (Also, attachments have a limited size and a limited set of extensions that are supported, too)
If you uploaded your images to a webhost, they would still be there. but if you did, you also attached them, which put them on the CH server, using up his disk space and bandwidth; the vast majority of attachments are fleeting; "here's a screenshot of the problem", or something; once the problem is solved, it's usually not necessary, and keeping the images around has a generally detrimental effect on the forum, as disk space is consumed on the server, bandwidth is used as web crawlers look at the image to extract metadata, which requires them to download it, etc.