What salty tasting water actually means
Salty water from a softener means one thing: brine is getting into your household water when it shouldn't.
Your softener uses a strong salt brine to recharge the resin beads that pull hardness out of your water. That brine is supposed to get fully rinsed down the drain at the end of each regeneration. When the rinse fails, salt hitches a ride into your taps.
The word intermittent is a big clue. If it tastes salty at certain times (usually early morning) and clears up later, that lines up with a regen cycle that isn't finishing its rinse.
The good news: most of these problems are cheap and fixable at home. The injector and drain line are the two most common offenders, and both are accessible on nearly every softener.
The bad news: a small percentage of cases trace back to worn control valve seals, and that's a pro-level repair or a replacement decision.
The usual suspects, in order
Start with the cheap, easy stuff and work your way in. Field techs do it this way for a reason: the most common causes are also the easiest to check.
A clogged injector (also called a venturi) is number one. It's a small plastic piece with a tiny orifice, and it does two jobs: sucking brine out during regen and rinsing it back out at the end. When it fouls with sediment or salt fines, the rinse goes weak and brine stays behind.
A slow or clogged drain line is a close second. If the softener can't dump brine fast enough, it backs up in the tank and ends up in your water. Kinks, uphill and submerged drain ends are the classic causes.
A stuck brine float or worn brine valve comes next. If the brine tank overfills, the softener draws more salt than it can rinse. You'll usually see a high water level in the tank as a tell.
Regen timing set wrong is easy to overlook. If your softener regenerates at 3 in the afternoon while you're running the dishwasher, you're pulling brine straight to your faucet.
Last and least common: a failing control valve. Worn internal seals let water cross between cycle positions, and brine leaks into service water. This one gets steadily worse and doesn't respond to cleaning.