The Crown Prosecution Service said 1,892 cases were dropped at court due to the "significant ill-health, elderliness or youth" of a defendant.
Another 439 cases were abandoned before the suspect was charged.
The CPS said the number of cases dropped for these reasons accounted for 0.3% of all prosecutions in 2014.
Such prosecutions dropped at court were 1,714 in 2013 and 1,402 in 2012. Those dropped before charge were 354 in 2013 and 128 in 2012.
Between January and March this year, 516 were dropped at court and 132 before charge.
The charity Victim Support said it was important that the decision not to prosecute was explained to victims.
Chief executive Mark Castle said: "Victims often fear that they will not be believed, so it can be many years before they come forward.
"It is critical that victims have the reasons behind a decision not to prosecute properly explained to them so that they understand that it does not mean they have not been believed."
The figures - released after a Freedom of Information Act request by the Press Association - did not specify the nature of the suspected offence.
The CPS said the decision to prosecute was made if there was both sufficient evidence and it was in the public interest.
A spokeswoman said: "The Code for Crown Prosecutors recognises that the more serious the offence, the more likely it is that a prosecution is required, and the age or ill-health of a defendant will be taken into account when deciding whether to prosecute."
In the case of former Labour MP Lord Janner, who has dementia, the CPS decided not to pursue historical child sex abuse claims against him.
The decision was overturned following a review, and a fitness to plead hearing is due to take place on 7 December. Lord Janner denies the allegations.

The Spaniard, 31, lost the first set but fought back to win 6-7 (3-7) 6-3 6-1 6-4 after three hours and 16 minutes.
Nadal saw 13 break points go begging before finally breaking the world number 59 after nearly two hours.
He dropped just five more games on his way to a last-16 meeting with Ukraine's Alexandr Dolgopolov.
"All the matches have been very tight - I am very happy," said Nadal.
"I don't know how many break points I had before I got the first one. Mentally, I fought a lot until that moment, then I think I played better."
Nadal could not land a telling return as the break points came and went against Mayer, and the Argentine took advantage by playing a fine tie-break to take the first set.
I am in the fourth round now. I don't think much about that.
When Nadal finally made the breakthrough at the 14th attempt, at 3-3 in the second set, he screamed "Vamos!" and his family and team celebrated in the stands.
The Spaniard had won all three previous matches against Mayer and went on to dominate after finally breaking.
There was a late flash of resistance when Mayer broke serve with Nadal trying to close out the match, but two games later the world number one sealed victory at 8.40pm local time.
Asked about a potential first-ever meeting with 19-time Grand Slam champion Roger Federer at the US Open in the semi-finals next week, he said: "I am in the fourth round now. I don't think much about that.
"It's a long way away. All the matches have been very tough.
"The only thing I am looking for is the practice tomorrow to keep working hard and focus on the match against Dolgopolov."
Third seed Federer booked his place in the last 16 with a clinical 6-3 6-3 7-5 victory over Spain's Feliciano Lopez.

A member of staff at Glenshee Ski Centre alerted SAIS to the slide on Glas Tulaichean, a 3,448ft (1,051m) Munro.
SAIS Southern Cairngorms said the full depth avalanche was filled with mud, rocks and large blocks of snow.
Another large slide was recorded at Creag Meagaidh in February.
The Sportscotland Avalanche Information Service (SAIS) provides avalanche hazard information reports for walkers, climbers and skiers from December to early April.
The service covers hills and mountains in Lochaber, Glencoe, Creag Meagaidh, Southern Cairngorms, Northern Cairngorms and Torridon.
More than 2,000 suspected criminals avoided prosecution in England and Wales last year because of their ill-health or age, figures have shown.
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Top seed Rafael Nadal overcame stubborn resistance from Argentina's Leonardo Mayer to reach the fourth round at the US Open in New York.
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The largest avalanche recorded by the Sportscotland Avalanche Information Service so far this season has been discovered in the Southern Cairngorms.