On December 1st, 2018 NCBI implemented a new system for searching that uses a personalised "API key". See the following post for more information.
The error shown below may occur in Geneious R11.1 and Geneious Prime if you not using an API key and you try to search all NCBI databases simultaneously†, if other Geneious Prime users on your local network are searching NCBI at the same time as you, or if you are downloading multiple blast search results simultaneously.
To prevent this error you should create and use a personalised NCBI API key.
See the following post for instructions on how to create and use your own API key with Geneious Prime.
† NCBI will allow Geneious users without an API key to make up to 3 requests to NCBI per second. If you are searching NCBI then make sure you expand the NCBI search list and select and search individual databases only. DO NOT select the top NCBI icon as Geneious Prime will then search all 9 databases simultaneously, which will exceed the request limit and cause the search to fail.