is that maintenance/feedback or support an integral phase of the SDLC in every software development or software engineering scenario
Maintenance is always an integral phase, as long as it is proposed the program or system will be run on real hardware. Real programs always have a certain risk of having defects, so as long as a program is not just written on a piece of paper without ever beeing run (for example, for educational purposes), there must be someone who fixes the defects when they prevent the program from beeing run at all.
Let's say that a software vendor signed up a contract with a customer who does not require their software to maintained or supported by the vendor.
A customer who contracts with a software vendor with no maintenance obligation could either
And even for the latter case, I would expect that someone could add a maintenance contract afterwards. So I cannot imagine a system where any kind of maintenance phase can be excluded reliably beforehand from its life cycle.
would the lifecycle repeat itself
Joel Spolsky's blog entry about Five Worlds mentions "throwaway software". It should be obvious that the "life cycle" of such programs is not a "cycle", and after the program was run once, it will probably not be needed any more. Note that even for throwaway programs, maintenance is part of the SDLC, since the program needs to run at least once.