It's common enough when the sentence is relatively short and the time to resolve an appeal might be longer than the sentence.
Many states don't allow bail if the conviction was for a serious or violent crime, such as rape or murder. Similarly, some states don't allow post-conviction bail if the trial court has imposed a lengthy sentence. For instance, a Florida court decided that a defendant's sentence of 14 years and 7 months made him a high risk to leave the state; he was therefore properly denied post-conviction bail. (Sims v. Wainwright, 307 F. Supp. 116 (S.D. Fla. 1969).) The reasoning for prohibiting bail in similar scenarios is straightforward: Defendants convicted of serious crimes or facing long prison terms are more likely to skip town to avoid what's awaiting them.
On the other hand, if the conviction is for a relatively minor crime or the sentence is short, trial courts are more likely to allow bail. Many jurisdictions have determined that bail should be available if a defendant's jail sentence is shorter than the amount of time it will likely tak to resolve the appeal (oftentimes a year or more). Otherwise, a defendant could win an appeal after having already served an entire jail or prison sentence.