Not able to change password through OWA in Exchange 2010

There is the possibility of user's mailbox exceeding the configured size limits. check them

Have you tried accessing through other browsers ?

Try resetting History and cache.

Try loading OWA light (you will get this option while logging in to OWA)

Try to loggin from different system and check, If working fine, Seems to be issue with browser,

More exchange level troubleshooting :

http://social.technet.microsoft.com/Forums/exchange/en-US/8a739f94-ae8b-482a-a850-b18894aa1708/your-changes-were-not-saved-because-of-a-microsoft-exchange-error-owa-exchange-2007-sp3?forum=exchangesvrclientslegacy

Have you enabled these features?  See article:
http://technet.microsoft.com/en-us/library/bb684904(v=exchg.141).aspx

No..Mailbox size is not exceedings..moreover checked for other user and getting same error.

Recently we have upgraded SP3 on exchange servers, is there any effect on Internal/External URL or OWA virtual directory.

let's assume that you have recently upgrade to sp then it fails.

can you run
get-owavirtualdirectory | fl *enabled

just to confirm the configuration is intact.

next is to find out whether your EWS, can you use OWA to create a rule? (just to make sure your EWS component is still working)

Has the password expired?
By default, changing expired passwords isn't possible.

Try the guide below to enable this feature if you haven't already.

http://technet.microsoft.com/en-us/library/bb684904(v=exchg.141).aspx

Below is the output of "get-owavirtualdirectory | fl *enabled"

DirectFileAccessOnPublicComputersEnabled         : True
DirectFileAccessOnPrivateComputersEnabled        : True
WebReadyDocumentViewingOnPublicComputersEnabled  : True
WebReadyDocumentViewingOnPrivateComputersEnabled : True
GlobalAddressListEnabled                         : True
OrganizationEnabled                              : True
ExplicitLogonEnabled                             : True
OWALightEnabled                                  : True
DelegateAccessEnabled                            : True
IRMEnabled                                       : True
CalendarEnabled                                  : True
ContactsEnabled                                  : True
TasksEnabled                                     : True
JournalEnabled                                   : True
NotesEnabled                                     : True
RemindersAndNotificationsEnabled                 : True
PremiumClientEnabled                             : True
SpellCheckerEnabled                              : True
SearchFoldersEnabled                             : True
SignaturesEnabled                                : True
ThemeSelectionEnabled                            : True
JunkEmailEnabled                                 : True
UMIntegrationEnabled                             : True
WSSAccessOnPublicComputersEnabled                : True
WSSAccessOnPrivateComputersEnabled               : True
ChangePasswordEnabled                            : True
UNCAccessOnPublicComputersEnabled                : True
UNCAccessOnPrivateComputersEnabled               : True
ActiveSyncIntegrationEnabled                     : True
AllAddressListsEnabled                           : True
RulesEnabled                                     : True
PublicFoldersEnabled                             : True
SMimeEnabled                                     : True
RecoverDeletedItemsEnabled                       : True
InstantMessagingEnabled                          : True
TextMessagingEnabled                             : True
ForceSaveAttachmentFilteringEnabled              : False
SilverlightEnabled                               : True
CalendarPublishingEnabled                        : True
OWAMiniEnabled                                   : True