Dear Sirs. Lately, it takes a very long time to receive confirmation mail for the client, and me to get the mail alert after the form is submitted

Hello dagss,

That is strange.

Please be noted that the notification emails are sent as soon as the form is submitted. I did check your form's notification email alert and did not find any issue with that. I also checked our bounce list and email logs and everything appears to be normal.

I have cleared your form cache from here. I would suggest you to test your form again and see if the emails are received without any delay.

If the issue persists, I would suggest you to use your own email address to send submission emails.  You should setup a custom "Sender E-mail" option. The following guides should help you:

http://www.jotform.com/blog/86-Send-Form-Emails-From-Your-Own-Email-Address-JotForm-Now-Support-SMTP 

http://www.jotform.com/help/236-How-to-use-Mandrill-to-Send-Emails-From-Your-Own-Email-Address 

Thank you!