okay, so i did some digging...
that solenoid, (2005-m-1) has some specifications that read as follows...
Johnson Electric 2005-M-1 Solenoid - 120VAC, 60Hz, Continuous Duty, 20.50 Ohms, 17.9W
now... if we plonk 20.5 ohms and 120v AC at 180 degrees phase angle into an AC current calulatormajigger we be looking at about 5.8 amps of peak current for that solenoid. this is assuming it never changes, but it does since it's a reactive device. so it may spike up to that, but settle lower after it's activated.
some other sites state it's value is somewhere about 4.8 amps draw... soooooo...
it may be worth it to bench test this solenoid with your volt meter setup for AC current reading and measuring the actual current draw of it. it may be that the although the schematic appears to have written ".5A" fuse... it could be perhaps, supposed to be a 5A fuse and the dot is an artifact of that documents age before it was scanned.. it may not be related.... who knows.... so unless another document or tag or something in your machine says that that fuse is supposed to be "0.5A" or "500mA" (like silk-screened onto the board or on a tag in the cabinet somewhere), a solenoid of that low of a resistance, by all rights... should have a larger fuse than 0.5 amps since it would obviously draw much more than that.
so, it's entirely possible the whole issue here... is simply... an improperly spec'd fuse.
using a 5 amp (slow blow) fuse on a circuit hauling 4.8 amps is perfectly spec'd. a slow blow MDL fuse can take 100% of it's rated load... indefinitely... and 200% of it's load for anywhere between 3 and 5 seconds before blowing.
so, dear watson you ask what to do?... yes, by my deductions, assuming this solenoid is the one originally in the machine... and knowing nothing and ignoring anything anyone may have done previously to the machine... and bench testing the solenoid's actually load (assumed to having a 4 or 5 amp load when activated)
a 5 amp slow blow fuse would be what is needed here, not a 0.5 amp.
*drops mic them promptly picks it up again and puts it away properly*