Search Contact icon is missing in request

Normally it is possible to change contact details name and account fields in an already created request.
The way to do it is to update the name by clicking on the "Search Contact" icon which is the one on the left:

But I have instances of requests where this icon is missing... Only the "Contact Info" icon shows and I cannot change the contact name nor the account.

(sorry for the ugly black lines masking my customer info)

Do you know a way to bypass this problem? Is there something that I can change in the request? Or should this be considered as a programing mistake (aka a bug)?

Thank you for your help,

Michel Denizot