Not only have I had that problem, but have seen times when texts just plain were not sent through.
The issue is likely not your phone but rather different cell companies Networks. The more repeaters a cell company saturates a given area with, the more through put their network has for voice and data. When a geographic area of a network becomes saturated with users, that network slows down, while other networks may continue to move along based on the availability of bandwidth. Depending on where you and the other person are and if you are on the same network, this can go from slightly slow to never delivered pretty fast. Most networks can throttle their bandwidth up to meet higher user demand a peak hours but as the receivers become bogged down, the network can still slow down.
As an example, 3 members of my family live in the same home on the same cell network (AT&T). We can text with no issues on Friday night. The 4th member lives on/near a college campus and is on a different cell company (T-Mobile). Texts between AT&T and the T-Mobile are often lost because the college campus becomes geographically saturated on the T-Mobile network due to a lack of repeaters AND the high number of users. As such texts get dropped first to protect the integrity of voice communications and to keep the network running. While this is happening, others who use another cell company (Verizon) have no issues because Verizon has saturated the geographic area with repeaters and provides better bandwidth throughput to it's customers. In that specific location, AT&T falls somewhere between Verizon and T-Mobile in the number of repeater but has far better service/coverage than T-Mobile does.
Or, it could be your phone. Keep an eye on it.
