Bold of you to put the concepts of "Homura" and "Lacking in mental fortitude" in the same sentence.
Not lacking, but even Homura is limited when it comes to mental fortitude, and if she searched alone she would need to be pretty much unlimited, as without Mami and Sabrina joining the search, she would need to search the whole Earth by eyesight, that's the kind of search that could take centuries, I could see Homura spending weeks in timestop for something like this, is if was a direct threat to Madoka she would probably have the mental fortitude to spend years or even decades in timestop, but while Homura has a really strong mental fortitude, it's not unbreakable, and a Clear Seed being stolen isn't a direct threat to Madoka, I really can't see her spending hundreds of years searching for it.
Sabrina is not mentally weak, but she's not as strong as Homura either, she could last days maybe even weeks, but without combining her power with Mami, her range is only a hundred meters, even with her range the search could take years, and I don't think Sabrina would last though that.
Sabrina and Mami combined could probably search the whole Earth in months, but Mami is currently rather mentally fragile, and the timestop seem to be especially freaky to her(probably due to her powers being about connecting to things, which make her feel the freeze all that more keenly) even the only hours long search for Oriko strained her, I don't think she would last for a month long search.
Everyone have limits, they might be extremely high limits, but they're there, and searching every inch of the Earth, is something I think is over even Homura's limits.
Seriously, if Homura did it solo, then even if she succeeded, I expect she would fill up multiple Clear Seeds in the progress, even if she could do it, it wouldn't be worth it, that long isolation would undo any progress, we have made on getting her to open up and allow herself to be human.