"The entire western world is facing an aging population, which is forcing all their pension funds and insurance companies to be structurally long long-dated government securities," he said, adding this trend started back in the 1980s and has been pushing yields down ever since.
In January, the Fed began to taper its quantitative easing program of $85 billion monthly purchases of mortgage securities and Treasurys by cutting $10 billion from the total, and it has stepped down the purchases by another $10 billion at each meeting since then. Starting in May, monthly purchases will be $45 billion.
After the 30-year U.S. Treasury yield touched a high of around 4.0 percent in January -- highest since mid-2011-- it has since come off to around 3.38 percent. The 10-year Treasury is yielding around 2.55 percent, down from around 3.0 percent in January.
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Others also expect this trend will keep long-end yields low.
"Long-dated bonds are going to perform well as U.S. defined benefit pension plans move out of (stocks) into bonds to hedge liabilities," said Steve Goldman, managing director at fixed-income manager Kapstream Capital. "You see that playing out in other countries with defined-benefit pension plans, like the U.K. and the Netherlands," he said. "That's the big, long-term story."
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European pension funds are certainly looking toward bonds, with around 20 percent saying they plan to increase bond allocations, according to a survey released last week of 1,200 European pension funds by consultancy Mercer.
Varnolt expects the trend to continue for another five years, even though bonds look expensive compared with stocks. He noted that buying a U.S. Treasury bond at 2.5 percent implies a price-to-earnings ratio of 40 times, compared with around 14 times for U.S. stocks.
Another factor likely pushing up bond prices, which move inversely to yields: "hyper nervous policy makers mean that at any sign of financial system instability, more money will flood the markets," Varnolt said.