Unable to get thread dump? Any ideas why my app blocks?

I have a basic java server app that has 100 worker threads that do simple HEAD requests on urls. I'm using HttpClient 4.x for this.

A few minutes into the run my program just freezes for a couple minutes and I cannot figure out why. Check out the screen shot of what visual vm monitor reports. You can see it flatline. During this time I'm unable to get a good thread dump and visual vm just freezes until it's unblocked. Does anyone have any ideas on what I can do to try and start debugging this guy?

Visual VM: http://tinypic.com/view.php?pic=2i915bs&s=7

Here is the output when I tried to take a jstack dump while it was frozen:

jstack -F 4325 
Attaching to process ID 4325, please wait...
Debugger attached successfully.
Server compiler detected.
JVM version is 16.3-b01
Deadlock Detection:

No deadlocks found.

Thread 4557: (state = BLOCKED)
Error occurred during stack walking:
sun.jvm.hotspot.debugger.DebuggerException: sun.jvm.hotspot.debugger.DebuggerException: get_thread_regs failed for a lwp
    at sun.jvm.hotspot.debugger.linux.LinuxDebuggerLocal$LinuxDebuggerLocalWorkerThread.execute(LinuxDebuggerLocal.java:152)
    at sun.jvm.hotspot.debugger.linux.LinuxDebuggerLocal.getThreadIntegerRegisterSet(LinuxDebuggerLocal.java:466)
    at sun.jvm.hotspot.debugger.linux.LinuxThread.getContext(LinuxThread.java:65)
    at sun.jvm.hotspot.runtime.linux_amd64.LinuxAMD64JavaThreadPDAccess.getCurrentFrameGuess(LinuxAMD64JavaThreadPDAccess.java:92)
    at sun.jvm.hotspot.runtime.JavaThread.getCurrentFrameGuess(JavaThread.java:256)
    at sun.jvm.hotspot.runtime.JavaThread.getLastJavaVFrameDbg(JavaThread.java:218)
    at sun.jvm.hotspot.tools.StackTrace.run(StackTrace.java:76)
    at sun.jvm.hotspot.tools.StackTrace.run(StackTrace.java:45)
    at sun.jvm.hotspot.tools.JStack.run(JStack.java:60)
    at sun.jvm.hotspot.tools.Tool.start(Tool.java:221)
    at sun.jvm.hotspot.tools.JStack.main(JStack.java:86)
    at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
    at sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:39)
    at sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:25)
    at java.lang.reflect.Method.invoke(Method.java:597)
    at sun.tools.jstack.JStack.runJStackTool(JStack.java:118)
    at sun.tools.jstack.JStack.main(JStack.java:84)
Caused by: sun.jvm.hotspot.debugger.DebuggerException: get_thread_regs failed for a lwp
    at sun.jvm.hotspot.debugger.linux.LinuxDebuggerLocal.getThreadIntegerRegisterSet0(Native Method)
    at sun.jvm.hotspot.debugger.linux.LinuxDebuggerLocal.access$800(LinuxDebuggerLocal.java:51)
    at sun.jvm.hotspot.debugger.linux.LinuxDebuggerLocal$1GetThreadIntegerRegisterSetTask.doit(LinuxDebuggerLocal.java:460)
    at sun.jvm.hotspot.debugger.linux.LinuxDebuggerLocal$LinuxDebuggerLocalWorkerThread.run(LinuxDebuggerLocal.java:127)

I've seen several bug reports about jstack on Linux with a similar trace: