Martin O'Hara stepped down as the head of Victoria University in Kampala in November last year.
Lesley Mearns, Victoria's dean of business, resigned in January, and the vice-chancellor's wife, Nora O'Hara, who led a foundation programme at the university, left in December.
Edulink, the education services company based in Dubai that financed the new institution, said that Victoria was a "success story", while Buckingham said it continues to back the venture and insisted that the university was functioning well.
Misho Ravic, chief executive of Edulink, said that the company had "provided all necessary support to Victoria University in a timely fashion".
"All required staff were recruited in time. No classes were delayed due to staff shortage," he said.
He cited a report produced by Buckingham after an inspection of Victoria in January, which said that "staff had all worked together to make sure that the students had not been disadvantaged...the overall impression is of [a] well-organised, well-functioning institution".
Dr Ravic further said that the report found that only one of the 60 students who had enrolled in September had given negative feedback.
He added that Victoria won a citation in March as "best international university" at the Nairobi International Education Fair, and said that a recent inspection by the Ugandan National Council for Higher Education had not found any areas in need of improvement.
Like many other UK universities with outposts around the world, Buckingham has set up Victoria in order to offer its degrees to foreign students on their own doorstep. The university has said that it will charge Ugandan students less than a fifth of what they would pay to do the same courses in the UK.
Buckingham, the UK's only private university, offers business, accounting and computing undergraduate degrees at Victoria as well as one-year foundation programmes.
Speaking last year, Professor O'Hara said Victoria aimed to have 4,000 students on its books in five years' time, with long-term plans to expand to between 12,000 and 15,000 students.
Under the terms of the partnership, Buckingham has the final say over staffing and takes a cut of tuition-fee income.
Frances Robinson, director of international programmes at Buckingham, said that the university was committed to Victoria and was planning to introduce a new programme in media, communications and journalism as well as a part-time MBA this September.
Dr Robinson visited Victoria in January and said it had been a "great relief to find the situation was under control".
She said she had given Edulink a list of issues to address, including maximum class sizes and contact hours, and that the firm had since "pulled the stops out" and further staff appointments had been made.
Dr Robinson said that as of January, 90 undergraduates had been confirmed as enrolled, 66 of them on Buckingham programmes, while a further 89 had enrolled on the foundation course.
These numbers could turn out to be higher, she said, as some students were still awaiting final registration because they had not yet provided all required documentation.