MPH1980

Easy - and this is a 'possible', not a 'certain' - but go with me:

Supplier has to make a change in their software system - they are on a regular release cycle - change is requested at the beginning of said cycle. Assume it's software as a service, assume a 6-8 week release cycle - we're down 2 months already and that's assuming the change is made at the right moment of the cycle and is included in that release.
Customer (in this case BA) has to wait for the change to hit production ... now assuming it's SaaS and there's no requirement for BA to deploy on their own hardware ... BA will then want to test the change in their QA/sandbox environments. Now you have to assume this particular change isn't top of BA's pile of to-dos ... so chances are that once the release goes in - there'll be at least a week or two's lag before the QA/whoever team get around to trialing the change. Once they've run through their 20-30 testing scenarios (assume one person on it - so a week) - it'll then go to change control to get permission to alter in production. So assume we're at 3 months by now.
That'll be a weekly committee or so and chances of getting the QA to end right the day before the committee is virtually 0 - so instead assume you have to wait a week ...
Then it'll get included in a change set ... so maybe a week after that.

Low and behold we're at 4 months and we're on a happy path.

If it's running on BA's own hardware you have to wait for the upgrade in a test environment, full regression to make sure nothing else is broken, a perf test (if they are sensible) before it's promotion to a production environment. You could easily add 2 months onto that cycle just for that.