In fact, they continue to play a huge role in sustaining the brand's leadership of the premium lager market. So why should Stella's InBev owner give even a passing thought to moving the global account out of Lowe Worldwide?
The knee-jerk answer would be that InBev has grown progressively more nervous about its association with the wounded animal that Lowe London has become. When a flagship client such as Tesco heads for the door, other clients wonder if they should be doing the same.
While there may be some truth in this, it is curious that InBev, which has remained loyal to Lowe despite its recent tumultuous history, should consider moving the Stella business now. What is more likely is that Lowe has fallen victim to the international muscle-flexing at InBev.
A year ago, it emerged the company was planning to make the Brazilian brew Brahma the world's first truly global beer brand, with advertising to match. InBev seems determined to make the most of its opportunities in what is a highly fragmented market, so a move towards a cohesive global campaign for Stella should not come as a surprise.
Of course, it is easy to get sentimental about Stella and its association with Lowe. Stella is the agency's oldest account, having arrived as part of Whitbread when the agency launched in 1982. Since then, probably no other piece of business has better encapsulated Lowe's creative culture. Its departure at this time could hardly be more poignant.
Nevertheless, there are sound reasons why InBev should proceed with caution.
The "reassuringly expensive" line has served Stella well in the UK, where sales are higher than in all other markets combined.
It is one thing launching Brahma globally with a clean creative slate. With Stella, that is not necessarily the case.