One-third of calls to the Department of Veterans Affairs’ suicide-prevention hotline go unanswered, according to a former VA official who ran the hotline.

President Barack Obama spoke of suicide and suicide prevention at the CNN town hall with military service members and families Wednesday night.

The VA’s suicide-prevention workers “spend very little time on the phone or engaged in assigned productive activity.”

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Obama encouraged depressed veterans to call the hotline and to get help. But at the same time, the Associated Press reported that bad work habits and other issues prevent all calls from being answered.

Some hotline workers handle fewer than five calls per day and leave before their shifts end — even as crisis calls have increased sharply in recent years, said Greg Hughes, the former director of the VA’s Veterans Crisis Line, according to a report in the Associated Press.

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Hughes said 35-40 percent of calls go unanswered and then get kicked over to backup centers where there is less training.

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The disclosure by Hughes was made in an internal email.

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Hughes wrote that workers “spend very little time on the phone or engaged in assigned productive activity.”

Coverage at the crisis line suffers “because we have staff who routinely request to leave early,” he said, according to AP.

The crisis line dispatched emergency responders an average of 30 times a day last year and made 80,000 referrals to suicide prevention coordinators, according to a federal official.