The system failed to register pointer (PTR) resource records (RRs) for network adapter with settings

ipconfig /registerdns tried , issue still there

Did you check whether a pointer record for 192.168.1.13 exists in your reverse lookup zone for 192.168.1.0?
If so, did you
- delete it
- wait for DNS replication
- register it again?

The PTR record exists

Then this entry has probably been created by another machine at some point.
- delete the PTR record on one DNS
- wait until the deletion has replicated to the second DNS server
- run ipconfig /registerdns on the server

OK , but will have to schedule that during the night since this is actually our Exchange server

If the name that the PTR entry is pointing to is not the name of the server it should be, then you should be able to delete the record immediately, since it is obviously incorrect.

Another option:
Set the View entry in the DNS manager to Advanced, then open the properties of the "13" PTR record. Go to the Security tab, check the permissions there.
Add the computer account of the Exchange server with Full permissions (make sure that in the object picker, you enable the object type "Computer").
Remove any other single computer account (the ones ending with $) from the security list (there's probably one other entry there, and this will be the machine that registered the PTR record).

I did not find any machine account , all are user and group accounts

I added an entry for the machine account with full control , I have also executed the "ipconfig /registerdns" command once again.Will wait for an entry in the event viewer

The PTR record details matches that of the server (hostname and IP address)

The same error is being logged every 24 hours !

Have you tried deleting the PTR record for 192.168.1.13  from 192.168.1.10, and then recreating it from the server?
Is this the only machine that has this problem, and are there other PTR records in this zone?
Are dynamic updates enabled for this zone?

Thanks oBdA,

1. This is an AD integrated zone 
2. Dynamic Updates are enabled "Secure Only" 

Yes; if it fails to re-register, you can still add the record again manually, so you'll have nothing lost.
And again: is this the only machine that has this problem, and are there other PTR records in this zone?

Looks like event ID last appeared on 28th of september , may be after adding the machine account as per your suggestion

Here is the last DnsApi event ID 11160:

______________________________________

Event Type:    Information
Event Source:    DnsApi
Event Category:    None
Event ID:    11160
Date:        28-Sep-09
Time:        9:59:18 AM
User:        N/A
Computer:    hostname
Description:
The system failed to register pointer (PTR) resource records (RRs) for network adapter
with settings:

  Adapter Name : {357970E8-A46D-48D0-A068-696CDD521B95}
  Host Name : hostname
  Adapter-specific Domain Suffix : domain.LOCAL
  DNS server list :
        192.168.1.10, 192.168.1.11
  Sent update to server : 192.168.1.10
  IP Address : 192.168.1.13

The reason that the system could not register these RRs was because of a security related problem. The cause of this could be (a) your computer does not have permissions to register and update the specific DNS domain name set for this adapter, or (b) there might have been a problem negotiating valid credentials with the DNS server during the processing of the update request.

You can manually retry DNS registration of the network adapter and its settings by typing "ipconfig /registerdns" at the command prompt. If problems still persist, contact your DNS server or network systems administrator.

For more information, see Help and Support Center at http://go.microsoft.com/fwlink/events.asp.
Data:
0000: 38 23 00 00               8#..    



Today , I attempted your last suggestion to manually remove the PTR record and then running ipconfig/ registerdns but the following events were logged:

________________________________________________________
Event Type:    Warning
Event Source:    DnsApi
Event Category:    None
Event ID:    11197
Date:        10-Oct-09
Time:        9:24:19 PM
User:        N/A
Computer:    hostname
Description:
The system failed to update and remove host (A) resource records (RRs) for network adapter
with settings:

  Adapter Name : {357970E8-A46D-48D0-A068-696CDD521B95}
  Host Name : hostname
  Primary Domain Suffix : domain.LOCAL
  DNS server list :
        192.168.1.10, 192.168.1.11
  Sent update to server : <?>
  IP Address(es) :
    192.168.1.13

The reason the update request failed was because of a system problem. For specific error code, see the record data displayed below.

For more information, see Help and Support Center at http://go.microsoft.com/fwlink/events.asp.
Data:
0000: 51 27 00 00               Q'..    
_______________________________________________

&
___________________________________________________

Event Type:    Information
Event Source:    DnsApi
Event Category:    None
Event ID:    11191
Date:        10-Oct-09
Time:        9:24:19 PM
User:        N/A
Computer:    hostname
Description:
The system failed to update and remove pointer (PTR) resource records (RRs) for network adapter
with settings:

  Adapter Name : {357970E8-A46D-48D0-A068-696CDD521B95}
  Host Name : hostname
  Adapter-specific Domain Suffix : domain.LOCAL
  DNS server list :
        192.168.1.10, 192.168.1.11
  Sent update to server : 255.255.255.255
  IP Address : 192.168.1.13

The system could not remove these PTR RRs because because of a system problem. For specific error code, see the record data displayed below.

For more information, see Help and Support Center at http://go.microsoft.com/fwlink/events.asp.
Data:
0000: 51 27 00 00               Q'..    
__________________________________________________________

Any idea please?