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.
More than 2,000 suspected criminals avoided prosecution in England and Wales last year because of their ill-health or age, figures have shown.