Here's the thing; photobucket doesn't put your pic on these forums. These forums ask photobucket for the image, when you load the page. That's all any image host can do.

When you take your images off photobucket, it's not there when the page has to load, and the forums ask photobucket for the image.

The image has to stay online, or else wherever you've linked to it will not be able to find it. One way you can keep your image online is by using the file manager to attach the image to a post, then using that link to display the image. LDW does not appear to have an issue with hosting files meant for the forum on their servers indefinitely.