I thought the fuse was loose so I was trying to tighten it... Hence the jiggling.

Let them stay at your place tonight and call an electrician in the morning. You might not burn the house down. You might just fry every device with electronics in the house. (Ask my spouse how that works!)

Long distance diagnosis is impossible, especially without photos, but I'll cite a similar experience I'm familiar with. It happened about 50 years ago.

This was a plug (Edison base) fuse making a distinct humming and buzzing noise for weeks or months. Maybe the fuse was a little loose, or maybe the wire connection to the fuseholder's terminal wasn't solid.. in any case, the contact was poor somewhere. The connection was actually arcing. This eroded the contacts further, making things worse. Eventually the intense heat that resulted actually melted the fuseholder.

Fortunately, the arcing and molten metal were contained by the fusebox, a large, ancient, very solid closed-front box. If they'd reached the cardboard boxes stored nearby, the house would have probably gone up in flames.

In your case, there's a good chance that the entire panel will need to be replaced. Unless you're thoroughly experienced with electrical work, including installing main panels, don't try to fix this yourself. And for goodness sake, quit jiggling that fuse!

Open the main switch to shut off all power in the house. In an old fusebox, that could be a lever switch, or it may require opening the door, pulling out a cartridge fuse holder marked MAIN, and reinserting it upside down, so that the word OFF is right side up.

If you can't figure out how to open the main, call the power company. They'll know what to do, and can even pull the meter if necessary. Then use only battery powered lights and appliances until you can get this checked out by a licensed pro.

This requires an electrician. It's archaic wiring and in bad condition.

The fuse looks good. :) If you only get sporadic contact while installing the fuse I suspct the contacts in the fuse holder are corroded or damaged and not making a good connection to the contacts on the fuse. DavidR provides a gret response on what is likely happening and from the picture I'd agree that replacement is the best advice for this situation.

The fuse is the least of the problems. There's insulation missing from the disconnect knife switch and the bushings are gone from a couple of the box entrances. The insulation on the conductors also looks like it may have been compromised.

I confess that I don't recall ever seeing a panel like this before.

I can't be sure, but it looks like that knife switch is supposed to be linked with a fiber insulator to the rod at the bottom, which I would guess is activated by a shutoff lever on the side of the panel. So, there is presently no safe way to open the feed to this panel. Not good.

Also, the fuse is feeding what appears to be old type R AWG14 wire, probably going to a knob and tube circuit. AWG14 should be fused at 15 amps, but the fuse is 30 amps, providing inadequate overload protection.

This is a fire just waiting to happen. Please, call the power company and get this hot mess disconnected ASAP, then get a qualified, licensed pro in to replace it.