I did not know that new issues were only sold half day. I would have thought just the opposite. Since stamp collecting was high in popularity during that time. But I can see where half day sales would help boost enthusiasm for the new issue.
I suppose it is possible that the sales counter was only open for half a day given that the capital 'city' of the Virgin Islands, Charlotte Amalie (formerly called St. Thomas) only had a population of about 7,400 and so local demand for a post office to be open would not likely have been very strong. That would have been combined with the need for the small handful of postal workers in such a small post office to process the vast numbers of first day covers that inundated them rather than standing at the counter waiting for customers. I would guess that the postmaster would have pulled everyone into processing first day covers as soon as he was able to do so. I found a record from December 16, 1939 (the day after the first day) that says First day covers were dispatched the same day by steamer to San Juan, Puerto Rico. Covers that had postage of at least 10 cents (such as a block of 4 of these 3 cent stamps) were put on an aircraft on December 16 at 9 o'clock in the morning and were due to arrive in Miami. Florida by 5 o'clock that evening. Covers with less than 10 cents in postage were sent by boat to New York City and were due to arrive there by December 20. For the cover shown in the first post, it has 21 cents in postage so it would have been on the plane from San Juan to Miami where it would have been sent to Cristobal, Canal Zone on the next regular passenger and mail service flight on Foreign Air Mail route number 5 (FAM 5) which was provided by Pan American Airways. The plane from San Juan, Puerto Rico to Miami, Florida would also have been a regular Pan American Airways mail and passenger service flight. I agree that it is unfortunate that the recipient tore the envelope open at the left. It is also unfortunate that the sender mangled at least two of the stamps (the ones at the upper right). I do like the nice vignette at the lower left of the envelope.