This article in Nature in August presented a succinct, accessible, informative summary of what we know and don't know about immunity to SARS-CoV-2 (it even prominently quotes my University of Pennsylvania colleague John Wherry!)
There are media reports of anecdotal evidence of reinfections and waning antibody levels that have raised concerns about lack of durable immunity and alarm that vaccines will not work.
This article puts these results in perspective, highlighting that neither of these facts are surprising to immunologists and neither means that vaccines won't work.
A few summary points:
They are observing strong immune responses to the virus in most people, including high antibody levels as well as T-cell responses.
Antibody levels waning does not necessarily mean loss of immunity -- it is not clear how much antibody is needed for effective response, and memory B-cells can regenerate antibodies when exposed again in the future.
There is evidence of strong T-cell immune response, which is not necessarily accompanied by antibodies, and this can endure long after infection.
Not all immunity is "sterilizing" immunity, meaning that the person will not get infected again, but can just predispose the person for mild symptoms/asymptomatic disease and fast recovery. This may be enough to take the edge off of the virus.
There is also evidence of cross-immunity in the form of T-cell response presumably from exposure to other coronaviruses -- it is not clear if that leads to sterilizing immunity or not.
The conclusion is that we have a lot to learn about the immune response to SARS-CoV-2 and length and form of immunity it produces, but there are enough positive signs that it is reasonable to expect that a vaccine can be effective and the virus can be brought under control.