This problem has been apparent for some time and the Army has been advertising vigorously for recruits, both to make up the shortfall and to cover normal turnover. These advertisements are, strikingly, not of the Action Man variety. Instead of looking for Schwarzeneggers, the billboards call for "15,000 maintenance men", or "15,000 security guards", or even "15,000 carers".
Carers? Yes, for the age of peacekeeping and large-scale humanitarian operations, the Army wants people who can "combine combat readiness with compassion".
Today's soldier, then, must be caring and intelligent, capable of handling tricky diplomatic situations in, for example, Bosnia, involving civilians of all kinds speaking a foreign language or, indeed, several foreign languages. He or she must also be capable of operating and maintaining complex technical equipment. Oh, and, if necessary, be ready to run towards gunfire and stick a bayonet into a soldier from another country who may be screaming for mercy.
Do such men and women exist? Are we asking the impossible? Two centuries ago, Edmund Burke wrote of the "rapacious and licentious soldiery". That army was a force separate from society, almost a caricature of it, exaggerating its worst traits. Soldiers were killers, more or less trained for the task, often violent and drunken when off duty, and heartily disliked for it.
One century ago, Kipling wrote memorably of the cruel public schizophrenia about soldiers: "For it's Tommy this, an' Tommy that, an' 'Chuck him out, the brute!'/ But it's 'Saviour of 'is country' when the guns begin to shoot."
Since then we have seen two world wars and the rise of mass armies - people's armies - in which Tommy was a different sort of man, reflecting and still part of the society from which he came. Generations of British people learnt a different view of the army then, a more comfortable one, but most of us have missed the most recent change.
Since the end of the Cold War, in many developed countries, the great conscript forces are gradually being replaced by small, professional armies to fight what Clausewitz called "cabinet wars". Even France, which invented conscription with the first levee en masse in 1793, recently announced it was ending it, and Russia, too, appears to be focusing on a much smaller, professional force. The effect of this is that the problem of alienation - of armed forces drawing apart from the rest of society - is growing.
The British Army has been all-professional for longest, since the 1960s. It prides itself on being an elite, yet the alienation is there for all to see. Go into Aldershot on any Saturday night and you will find soldiers behaving as badly as any young men of their age. They even believe that, being soldiers, they have a particular right to act this way. They may not be right, but that is how they are.
The British Army is no longer a people's army; it has reverted to a form which Kipling or even Burke might recognise. It is a relatively small force, brutalised and trained to kill and only kept in order by draconian discipline - discipline which can fail as we saw only a few weeks ago, when three British soldiers in Cyprus were convicted of battering the Danish tour guide Louise Jensen to death while drunk. It was an appalling breakdown of discipline, but it reminded us, in an extreme and lurid fashion, of a side of soldiering far removed from the familiar peace-keepers of Bosnia, of the hard-drinking hard men, of Tommy "the brute".
Of course soldiers don't have to be thugs. Victorious wars have, in the main, been fought by ordinary people, not psychopaths. And while it would be going too far to say that all of today's special forces soldiers - real, professional killers - are in bed with a cup of cocoa at 10pm every night, a surprising number of them are. Those I have met are quiet, smart, polite and unbelievably ordinary.
I shall never forget the soldiers who pulled me out of a crashed car in Bosnia. My colleague wanted to take a photograph as a record. They declined to appear in it. Only later did I realise why: they were "Joint Commission Observers" - SAS.
The British Army's view is that well-disciplined soldiers can be persuaded, or taught, to do most things. It tries to prepare its troops for any eventuality. Before Northern Ireland, they train for that environment. They train specifically for Bosnia. And in the run-up to the Gulf war, they trained for bloody, large-scale armoured warfare in the desert.
But it is training - specific, thoughtful training - that enables soldiers to switch from one task to another, and the difficulty in future, with limited manpower, may be doing this quickly enough. An Army recruited for peacekeeping, as the latest campaign suggests, may not provide the best warriors.
In Bosnia, the Army really wants policemen and policewomen: well-educated, adaptable people who can think and take responsibility on their own. In situations such as the Falklands war, where a battalion might have to attack an enemy force four times its size, well-educated, adaptable people used to taking their own decisions may well politely decline opportunities for posthumous medals.
Perhaps we need different kinds of soldiers to do different jobs - regiments of Jekylls, and regiments of Hydes.
The writer's latest book, 'Knights in White Armour: The New Art of War and Peace', will be published by Hutchinson next month.