EVALUATION

Note as per 5068368 there is no explicit requirement that a sleep last for at least the amount of time requested, so an early return is valid according to the JLS third edition.

That said, the very short sleeps that have been observed seem to fall outside the realm of expected behaviour and so require further investigation. It is unclear at this stage whether the problem is with the sleep, or the use of System.nanoTime to measure the elapsed time.
                                     

EVALUATION

First of all the test is not quite accurate, System.currentTimeMillis has
a granularity of 10ms, if the code is changed to use System.nanoTime. 
The VM (1.6.0-b55) does sleep for the required time with no signs of chronic
insomnia, as observed earlier.

[K:/L/A/HS/6313903] cat ut.java
public class ut {
    public static void dojuc()  throws InterruptedException {
        //long t0 = System.currentTimeMillis();
        long t0 = System.nanoTime();
        java.util.concurrent.TimeUnit.MILLISECONDS.sleep(3);
        //System.out.println("timeunit:" + (System.currentTimeMillis()-t0));
        System.out.println("timeunit:" + (System.nanoTime()-t0)/1000000);
    }
    public static void main(String[] args) throws Throwable {
        for (int i = 0 ; i < 10 ; i++)      {
             dojuc();
        }

    }
}
[K:/L/A/HS/6313903] java ut
timeunit:15
timeunit:1
timeunit:3
timeunit:3
timeunit:3
timeunit:3
timeunit:3
timeunit:3
timeunit:3
timeunit:3

However the testing revealed that the first time it sleeps, it seems to 
sleep for a long time, and the second time its for a very short time
and then it stabilizes to 3msec (perhaps thread scheduling/clock transients), 
this is also consistent with a native test case, as follows:

[C:/XXXX] ./Insomnia on
MIN res : 1
MAX res : 1000000
sleepy time = 3, elapsed time=12.08533 secs HighRes(on)
sleepy time = 3, elapsed time=0.42910 secs HighRes(on)
sleepy time = 3, elapsed time=3.85608 secs HighRes(on)
sleepy time = 3, elapsed time=3.86530 secs HighRes(on)
sleepy time = 3, elapsed time=3.86613 secs HighRes(on)
sleepy time = 3, elapsed time=3.86697 secs HighRes(on)
sleepy time = 3, elapsed time=3.86865 secs HighRes(on)
sleepy time = 3, elapsed time=3.86530 secs HighRes(on)
sleepy time = 3, elapsed time=3.86166 secs HighRes(on)
sleepy time = 3, elapsed time=3.86837 secs HighRes(on)
Hit CR to coninue......

Here is the native test case:
// Insomnia.cpp : Defines the entry point for the console application.
#pragma comment( lib, "winmm" )

#include <iostream>
#include <tchar.h>
#include <windows.h>


class HighResolutionInterval {
  // The default timer resolution seems to be 10 milliseconds.
  // (Where is this written down?)
  // If someone wants to sleep for only a fraction of the default,
  // then we set the timer resolution down to 1 millisecond for 
  // the duration of their interval.
  // We carefully set the resolution back, since otherwise we 
  // seem to incur an overhead (3%?) that we don't need.
private:
	static const int DEFAULT_RESOLUTION=1;
public:
  HighResolutionInterval(long ms) {
      MMRESULT result = timeBeginPeriod(DEFAULT_RESOLUTION);
  }
  ~HighResolutionInterval() {
      MMRESULT result = timeEndPeriod(DEFAULT_RESOLUTION);
  }
};

int os_sleep(long ms, bool highResMode) {
	HANDLE events[1];
	   events[0] = CreateEvent( 
        NULL,   // no security attributes
        FALSE,  // auto-reset event object
        FALSE,  // initial state is nonsignaled
        NULL);  // unnamed object


	int result = -1;
	HighResolutionInterval *phri=NULL;
	if(highResMode)
		phri = new HighResolutionInterval( ms );
	if (WaitForMultipleObjects(1, events, FALSE, (DWORD)ms) == WAIT_TIMEOUT) {
		result = -3;
	} else {
		printf("Error in WaitForMultipleObjects\n");
		result = -2;
	}
	delete phri; //if it is NULL, harmless
	return result;
}

double gethrTime(LARGE_INTEGER freq) {

	LARGE_INTEGER hrcount;

	if (QueryPerformanceCounter(&hrcount) != TRUE) {
		printf("Error: QueryPerformanceCounter\n");
		exit(-12);
	}
	
	return ((double)(hrcount.QuadPart)/(double)(freq.QuadPart))*1000;
}
int _tmain(int argc, _TCHAR* argv[]) {
	bool highResMode = (argc > 1 && _stricmp(argv[1],"on") == 0) ? TRUE : FALSE;
	long ms = ((argc > 2 && *argv[2] != '\0') ? atol(argv[2]) : 3L);
	TIMECAPS tc;
	memset(&tc,0,sizeof(tc));
	if (timeGetDevCaps(&tc, sizeof(TIMECAPS)) != TIMERR_NOERROR) {
		printf("Error: timeGetDevCaps failed\n");
		exit(-1);
	}

	printf("MIN res : %d\n", tc.wPeriodMin);
	printf("MAX res : %d\n", tc.wPeriodMax);

	LARGE_INTEGER freq;
	if (QueryPerformanceFrequency(&freq) !=	TRUE) {
		printf("Error: QueryPerformanceFrequency\n");
		exit(-10);
	}
	if (freq.QuadPart == 1000) {
		printf("Error: QueryPerformanceFrequency resolution	not	supported\n");
		exit(-11);
	}

	for (int i = 0 ; i < 10 ; i++) {
		double t0 = gethrTime(freq);
		os_sleep(ms, highResMode);
		double t1 = gethrTime(freq);
		printf("sleepy time = %d, elapsed time=%2.5f secs HighRes%s\n", ms, t1-t0, (highResMode) ? "(on)" : "(off)" );
	}
	printf("Hit CR to continue......\n");
	while (getchar() != '\n');
	return 0;
}

based on the above test result,I am downgrading this bug to P5 and will be 
reporting this to Microsoft through the established channels, until then.....