RD Connection Broker randomly fails to process connection requests

Question

The RD Connection Broker is a Windows 2008 R2 server. It's been running without issues for 3 years. It handles three RD servers also Windows 2008 R2.
Starting yesterday some users - not all - no longer can log on using the farm name. If the RDP file is set up to point to the server they were disconnected from then they get their session back.
There is only one error in the TerminalServices-SessionBroker log:
Log Name:      Microsoft-Windows-TerminalServices-SessionBroker/Operational
Source:        Microsoft-Windows-TerminalServices-SessionBroker
Date:          8/19/2014 15:04:18
Event ID:      802
Task Category: RD Connection Broker processes connection request
Level:         Error
Keywords:     
User:          NETWORK SERVICE
Computer:      NJDC1.nj.kearfott.com
Description:
RD Connection Broker failed to process the connection request for user NJ\a.davis.
Load Balancing failed OR Specified endpoint could not be found.
HRESULT = 0xfffffc0a.
Event Xml:
<Event xmlns="http://schemas.microsoft.com/win/2004/08/events/event">
  <System>
    <Provider Name="Microsoft-Windows-TerminalServices-SessionBroker" Guid="{D1737620-6A25-4BEF-B07B-AAC3DF44EFC9}" />
    <EventID>802</EventID>
    <Version>0</Version>
    <Level>2</Level>
    <Task>101</Task>
    <Opcode>11</Opcode>
    <Keywords>0x2000000000000000</Keywords>
    <TimeCreated SystemTime="2014-08-19T19:04:18.882662400Z" />
    <EventRecordID>1971452</EventRecordID>
    <Correlation />
    <Execution ProcessID="2388" ThreadID="1308" />
    <Channel>Microsoft-Windows-TerminalServices-SessionBroker/Operational</Channel>
    <Computer>NJDC1.nj.kearfott.com</Computer>
    <Security UserID="S-1-5-20" />
  </System>
  <UserData>
    <EventXML xmlns:auto-ns3="http://schemas.microsoft.com/win/2004/08/events" xmlns="Event_NS">
      <param1>NJ\a.davis</param1>
      <param2>0xfffffc0a</param2>
      <param3>8</param3>
    </EventXML>
  </UserData>
</Event>
The MS updates were installed last week so this issue did not happen immediately after the install.
Any help, pointers, ideas would be greatly appreciated

Answer 1

Thanks for replying, Dharmesh but I forgot to mention a couple of things:
1. There was only one 802 event and quite a few users who could not log on using the farm name for the RDP connection. This is still happening though the majority of the users have no problem logging on to the RD servers using the farm name.
2. Those who could not log on using the farm name could log on using a specific server name. I have not tried all the names because on the first day I had noticed that one server had no users on while the other two had lots. So when the first call came in
I pointed the user to the one server with the smallest load.
3. This is the first time this happens since I set up the farm.
4. This shouldn't matter but I had uninstalled IE 11 about a week before and reinstalled IE 9. 
5. Some users who logged on using the farm name have to be logged off as they can't log back on after a disconnect.
I had seen the first article before I posted. Looked ant the second. I'll have to study it because at the first glance it doesn't appear to have much to do with my issue.