Time flies.

Wouldn’t it be funny if the unwanted long-term care insurance (LTCI) business that sits in insurers’ “closed-block” businesses like an unwanted ex-spouse squatting in the cellar came back someday?

Most insurers with closed LTC blocks are keeping the numbers out of their earnings releases and supplements this quarter.

One exception has been Unum Group Corp., Chattanooga, Tenn. (NYSE:UNM).

Unum says premium revenue at its closed block of long-term care insurance (LTCI) business actually went up during the second quarter, to $157 million in the second quarter, up from $151 million in the second quarter of 2011.

The interest-rate-adjusted loss ratio, or ratio of claims to revenue, increased to 87.8%, from 84.3%, but ratio spiked up to 91.2% during the first quarter, and Unum was happy to see the decrease from the first quarter, company executives said during a conference call with analysts.

Total net LTCI reserves increased to $5.7 billion at the end of the quarter, from $5.4 billion at the end of 2011.

Premium persistency for the first half increased slightly, to 95.8%, from 95.6%.

Unum Chairman Thomas Watjen said during the Unum earnings call that the “extremely low rate environment” has been hurting the LTCI block as well as other Unum operations.

“That block will continue to be a challenge,” Watjen said.

Richard McKenney, the Unum chief financial officer, was not in a frame of mind to murmur sweet nothings about LTCI during the call.

Firming at the LTCI business is the result of rate increases that are only now starting to take effect, McKenney said during the call.

But all the pressures that have been squeezing the LTCI business “are still challenging,” McKenney said. “When I talk about improvement, it’s slight improvement over time. It’s nonmaterial improvement.”

McKenney also needed a lot of words to avoid really answering about whether Unum might have to add to the reserves backing the LTCI block.

But the block seems to be settling down and performing more the way Unum expects it to perform in the future, company executives said.

The current LTCI situation reminds me of an economic outlook luncheon I attended awhile back, maybe in 1991. Someone asked about the possibility of interest rates going up. An analyst at the table used a scenario in which rates went up 3 percentage points in a year as an example of an absurd scenario that couldn’t possibly happen. Then, of course, rates proceeded went up 3 percentage points.

If only rates would go up just 1 percentage point, or 2, in some kind of orderly fashion, with portfolio yields increasing but the economy somehow muddling along, maybe insurers would get their LTC businesses out of the closed-block cellar and back into the parlor.