The ambiguity actually comes in to play because
προσκαρτεροῦντες is a present participle. The present tense has so many different categories, such as descriptive, iterative, durative, tendential, historical, futuristic that there is some ambiguity. These categories come from a perceived need to fit the Greek language into English terms in order to understand it. They are helpful where context allows for it, but sometimes they lead to interesting translations.
Words like "continually" or "constantly" are a bit misleading because they could generally be either durative (an action that began in the past and is still occurring today) or iterative (happens periodically) and are attempts to bring out the "present" tense usage in what appears to be a past tense setting. As such, I'm not sure that we should place too much weight on the present tense in this case, other than that Luke was describing the state of things within the Jerusalem community.
So what does this all mean?
The participle itself is governed by the preceding verb ἦσαν (imperfect indicative of "to be") which leads me to believe that this is a periphrastic construction. As such, it is a "marked" way of highlighting the activity of "all these." They were continuing in (the?) prayers. Because of the periphrastic, I don't necessarily think that a 24/7 (durative/continuous) action is in view. It seems to be a way of reinforcing the steadfast and committed nature of the faith of the disciples in light of the Ascension.