Synchro's do not become shot within one second. When you have a grinding issue, not relating to the clutch, it is more than likely a bad blocking ring. The blocking ring is to slow/stop the gear you are wanting to engage, then the synchronizer locks it in place.
Most times when there is a grindage issue, you have a bad clutch, bad clutch cable/adjustment, or a bad blocking ring. If you keep grinding the gear(s), you will eat at the synchronizer, needing new ones if you want for a smooth shift. And if you fix your grinding problem, being the clutch or blocking ring, but not the synchro, you will have a notchy shift in that gear from there after. Another thing to cause notchy shifts would be the teeth on the actual gear, where the synchronizer engages with. When booth are worn down, a new blocking ring will not ensure a slick smooth shift, but only a grindless one.
If your grinding problem popped up out of nowhere, and you never had the symptoms of a bad blocking ring going out, like hard/notchy shifts and slight grinds on cold shifts, it's likely to be your clutch.....especially if you are smelling burnt clutch material.