It remains my belief that a continuing high reputation is only actually possible if a single domain is hosted on your own IP address. Anything else is pure luck that doesn't see a reputation downgraded even if it is for a short while.?
You've lost me there. Your ISP hosts rather a large number of domains, and may even out-source the service. (In your case, so far as I know Yahoo is completely independent of BT, but could be providing a badged dedicated "BT Yahoo" service. That is still out-sourcing).
I don't see what your IP address has to do with the subject. First, domains are not hosted on your IP address. Second, domains and email servers are different beasties, they don't need to be hosted at the same place. Third, in your particular case, unless you are on a BT Business connection you have a dynamically allocated IP address.
I don't understand the second sentence.
First of all let me say I have a high regard with your knowledge on a whole host of subjects and I can only assume on this occasion that I have not stated my position clearly. So let's try again.
Posting this message is not from the domain in question nor through the same ISP.
My comments relate to a BT Infinity broadband service used in conjunction with web hosting from a company that also handles our domain registration. The web site is on their servers together with the created email addresses. Our domain sits on a server that also hosts in excess of 500 other domains but of course we all share the same IP address.
Now on the email side of things POP3 points to the hosting providers server but for SMTP facilities it was strongly recommended that the ISPs SMTP server is used. The ISPs SMTP server, especially if it is BT, will always have a high reputation whereas the hosting provider's server will frequently, or permanently, have a low reputation, it all depends on what the other domain users on the same IP are up to.
For the record, it is a BT Business connection with a fixed IP provided as there is a need for home workers to access facilities in the office. These home workers have a laptop which they will bring to the office from time to time. It is our choice to use MS Outlook on those machines. The staff numbers do not warrant, nor is it affordable, to use a server.
If we use BTs SMTP server we are frustrated to find that the email client's configuration is different depending whether the laptop is in the office or used at home. I would stress this is BTs way opf doing things and is not the same as other ISPs approach which is through authentication which works no matter where you are geographically located or the ISP used.
If we use the hosting providers SMTP server the above issues do not surface but almost certainly that server's IP address will have a low reputation resulting in our emails being rejected in a number of cases. There as absolutely nothing we, or the hosting provider, can do about this low reputation.
Now I am pretty sure that other BT Infinity users must have been presented with this problem and I am interested to learn if they have found a solution. Hosting facilities are costing us an arm and a leg so we have not gone for a "cheap as chips" provider. Personally I am surprised that BT can't, or won't, offer a solution to this problem.
RobertOS response just muddies the water and introduces statements which IMHO are quite unrelated. But I could be wrong, after all I am just an end user struggling to get the best for other staff members.