If a client has accepted a caution is it still possible to appeal the decision that they were overpaid?

In principle I dont see why you can't but in most circumstances I would think you have an uphill struggle on your hands! What are the facts of your case?

As answered above, there is no problem making an appeal - a caution does not take away the right of appeal.

But, it may not necessarily be any more of an uphill struggle than any other appeal.

It's quite possible that a breach in one aspect, leading to a caution, will not be grounds that are at issue (directly) in an appeal.

For example, take this scenario for HB/CTB. A clmt is found to have undisclosed capital, but the clmt still has total capital not exceeding £16,000. An overpayment results. The LA takes a strong stance and offers a caution, which the clmt accepts. BUT, the clmt (or rep) spots an error in the calculation of the undisclosed capital (e.g. 10% disregard due on shares). The caution may, technically, be correct, but an appeal should succeed.

So, as suggested by SLloyd, more info / detail would make it easier to advise.