Bear with me as I know this sounds obvious, but have you topped the washer fluid up? The pickup for the rear washer is situated higher up in the washer fluid bottle than the headlight/front screen wipers. The rear will run out of fluid a significant number of uses before the fronts.
The check valve is located under the right hand side boot floor in the 850s, not sure if this is the same in the V70s. Also check behind the speaker panel in the D-pillar trim, may also be located there. This does clog up over time with contaminants/algae so could well be the cause.
Another thing to check is all your lines - sometimes they split by the boot hinge, or get chaffed on their path through the boot floor.
Lastly, check the nozzle. They clog up fairly frequently, which is first noticeable by the jet becoming less powerful, until its basically a dribble.
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1995 Volvo 850 T5 Estate (Manual)
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