Many users on the official Pikmin Bloom community forum and the subreddit /r/PikminBloomApp have had SMS or notification related bugs recently. A very popular official community forum post, in which users who participated in the closed beta are saying that the bug dates all the way back to April or May of this year, and that beta users have since been reporting this to the app's developer Niantic(of Pokemon GO fame) as a critical issue.
Users can currently work around the bug by force closing the app so that they can send SMS, but there's no guarantee that you'll receive all of your texts and notifications on time while using the app.
Today(saturday Nov 13th) was the first community day on the app, where points and rewards would be multiplied and you'd get a badge if you walked 10k steps while using the app.
I didn't experience delays in receiving SMS or notifications in my ~10h of use of the app so far (I do highly recommend it, great AR game). However, I sent 3 texts while walking, and realized hours later that they were still stuck on "sending".
Several reddit users have noted this could really cause major problems for people using SMS or notifications for time critical scenarios(a pregnancy for instance). Some frustrated users are trying to report the app to the google play store, in hopes that google will step in and make sure the bug is fixed.
Niantic has yet to provide any comment on this bug that I'm aware of.
Sources
Pinned reddit post:
https://reddit.com/r/PikminBloomApp/comments/qqyf0s/warning_the_pikmin_bloom_app_will_interfere_with/
Official Community forum bug report
https://community.pikminbloom.com/discussion/31/sms-sending-and-receiving-is-still-being-delayed-until-app-is-forced-stopped-or-uninstalled
Game screenshots [free reuse :^)]