‘All the gold and silver of the mountains are mine,’ fails to provide necessary funds, we will understand it to be time to suspend the publication.”
To me, Russell's comment is saying that the amount of funds they take in, is directly proportionate to the amount of approval they have from Jehovah. If the necessary funding fails to be provided, they will take that as a sign that Jehovah isn't backing them. If Jehovah isn't backing them, rather than solicit for money, they'd suspend or reexamine their current activities . If that is the case with the publishing of a magazine, it would be all the more so the case with the rest of their activities that also need funding to continue.
That was the premise this religion was originally founded on and it makes sense that if this is the true religion and it is being backed by Jehovah, then it would have everything it needs, all of the time. Didn't Jesus say he could even make the very stones cry out if need be, to get the preaching work done?