Glossary mode on View Block disappear once a letter is clicked
Found the step by step correct setting  from here.


Create a view with page to show desired content type  (PS: you must create a view page, event you only use the view block)
click on CONTEXTUAL FILTERS
add content title
Select this page override
Select Provide default value and type fixed value 
Enter "a" for default display only "a" word containing content and enter "all" for default display "all" content 
select Specify validation criteria:Basic
Click More AND check Glossary mode option
Set Character limit 1
save
Use Ajax "yes"


Now add a attachment


click on CONTEXTUAL FILTERS 
add content title
Select this attachment override
Click Display a summary
Click Unformatted and check Display items inline, under Separator add "-" or "|"
Set Attach to: page From ATTACHMENT SETTINGS
Set Inherit contextual filters: NO From ATTACHMENT SETTINGS
Use Ajax: Yes
Now save and run the page