The OP commented that this situation turned out to be a case of the recipient using Hangouts’s “block user” feature.
Many messaging websites will fail to deliver messages to other users with mysterious/inexplicable reasons or silently fail to deliver a message at times. If this happens, it is possible that the recipient has blocked you. To protect users, when a blocked user tries to send a message, the blocked user is not given a very specific error message. Or, perhaps, the recipient is made invisible to the sender or the message is silently failed instead of even showing an error. This is because the block feature is meant to be useful in the situation where the blocked user is harassing another user. Additionally, you may not be able to join any group conversations when any user in that group conversation has blocked you.
To people who consider using the “block” feature: the “block” feature is meant for handling users who endlessly harass or spam you who you are unlikely to want to contact again. If a person is annoying you but you intend to maintain a relationship with them, please consider not blocking that person. Many messaging websites offer a “mute notifications” feature. For example, in Hangouts, open a conversation. From there, click the gear icon, and uncheck Notifications. Your browser and devices will no longer bug you with messages on that conversation, but you must remember to re-enable Notifications for that user later. Or if all Hangouts interactions are troubling you temporarily, open the menu in the upper-left hand corner (☰), choose Settings (gear), and under Notifications open the dropdown Mute notifications for… and choose a time period. To unblock someone in Hangouts, open the menu in the upper-left hand corner (☰), choose Settings (gear), open Blocked people, locate the blocked user, and choose Unblock.
To people who end up blocked: understand that sometimes people use the “block” feature without understanding the ramifications. For example, one might block someone even if they intend to contact them in the future. The “block” feature may cause the person who used it to be confused and unable to find the blocked person. To reduce the chances that another user decides to block you, please be understanding of other users and respect any requests to be quieter. Before sending a message, consider that something which seems important and pressing to you may just be an annoyance to the recipient. Also consider being less “spammy” by, e.g., composing a complete thought when sending a message instead of sending a bunch of short messages (one meaningful notification is less annoying than a series of partial-thought notifications). It is better to behave considerately to avoid being blocked if you want to still be able to contact the other user when something important comes up.