@Tyk,
The water softening mechanism can become clogged with sediment > water still passes through the pipe going to water heater, but the timer mechanism is frozen. It might be possible to clean out the timer, but every gear would have to be restored like new. If sediment is the problem, your next softener should have a simple sediment filter installed before water enters softener.
Until then, here's some information that could help you understand the new water heater.
Gas heater: If you have a gas water heater, and your water is hard, burner efficiency can be maintained using a water softener. But efficiency can also be maintained by flushing the water heater every 6 months using instructions in the manual, or from the web. Frequent flushing will buy you time until new softener can be installed. Without a softener, and without flushing, hard water calcium deposits will lower efficiency of gas water heater by 6-8% within 2 years. Once deposits coat combustion surface at bottom of tank, efficiency cannot be fully restored simply because no tool can effectively restore the combustion surface.
Self-cleaning tanks and self-cleaning dip tubes claim to help stop sediment build-up, but water heater forum articles generally dismiss 'self-cleaning' as ineffective long term.
Electric heater: If you have hard water and an electric water heater, then efficiency can be maintained using a water softener. Frequent flushing will also maintain efficiency if you do not have a softener. Without a softener and without frequent flushing, hard water deposits build up inside tank but do not affect efficiency until they reach lower element. Vacuuming out the sediment and replacing lower element restores full efficiency on electric water heater since the bottom of tank can remain coated with sediment without affecting lower element efficiency that sits several inches higher.
However, there is a down-side to your water softener. Artificially softened water dissolves the water heater anode rod faster than if you have no softener. Your new water heater manual should have a section about anode rods and softened water. Once anode rod is dissolved, the water heater tank begins to rust, leading to why you replaced the last heater. You can prolong the life of your water heater by periodic inspection and replacement of anode rod > the rule of thumb is inspect anode every 2 years if you have a softener > every 3-5 years without a softener. Tanks with longer warranties generally have two anode rods. Using knowledge and maintenance, water heaters can last a very long time. U-tube has a video on replacing anode rods. Another source is
http://waterheatertimer.org/Replace-anode-rod.html