Without a steady flow of cash — either through donations or, ideally, more members — the off-leash dog parks enjoyed by thousands around the county won’t last through the year.

The parks, DOGPAW President Mark Fruechtel said, have a free-rider problem: Less than 10 percent of users pay for their upkeep, but the rest likely don’t even know the parks receive no taxpayer support.

“Most people are under the assumption that the county pays for it,” he said.

During busier months, between 5,000 and 7,000 people daily patronize the five parks operated by DOGPAW, or the Dog Owners Group for Park Access in Washington.

But only about 700 people are paying members of the private nonprofit, Fruechtel said. He estimates DOGPAW would need about 4,000 paying members to break even. A membership costs $25 per year.

Without some kind of income boost, the parks have enough resources to last only another nine months.