HONOLULU — On the shoreline of Hawaii’s most famous beach, a decaying structure attracts little attention from wandering tourists.

A few glance curiously at the crumbling Waikiki Natatorium, a salt water pool built in 1927 as a memorial to the 10,000 soldiers from Hawaii who served in World War I. But the monument’s walls are caked with salt and rust, and passers-by are quickly diverted by the lure of sand and waves.

The faded structure has been closed to the public for decades, the object of seemingly endless debate over whether it should be demolished or restored to its former glory. The latest plan is to replace it with a beach, more practical for the state’s lucrative tourism industry — and millions of dollars cheaper, according to state and local officials. They say a full restoration could cost nearly $70 million.

The corroding monument has challenged the community to maneuver a delicate question: How do we honor those who have served when memorials deteriorate and finances are tight?

The National Trust for Historic Preservation waged a 2½-year fight to restore the aging Tomb of the Unknowns in Arlington National Cemetery in Washington, D.C., when some people proposed replacing it. Far less disagreement surrounded a decision to update the War Memorial Opera House in San Francisco after a powerful earthquake in 1989.

In Greensboro, N.C., residents have been grappling with what to do with the city’s own decaying tribute to the soldiers of World War I.

The Greensboro World War Memorial Stadium hosted minor league baseball for decades and even served as a location for notable sports films such as “Leatherheads” and “Bull Durham.”

Yet, despite continued use by kids and college-level athletes, the structure is falling into disrepair.

The historic pebbled facade is falling off, and some of the bleachers are blocked off because of crumbling concrete, said David Wharton, a Greensboro resident who is fighting as a member of his neighborhood association to restore the structure.

It’s been a losing battle. The city chose to build a new stadium for minor league baseball instead of fixing up the old one.

As a classics professor at University of North Carolina-Greensboro, Wharton has a soft spot for historic places. But he recognizes there are many other priorities competing for the millions of dollars it would take to restore the stadium.

“The war was a long time ago,” Wharton said. “I don’t think it’s meaningful for most people.”