To Jasonlkk,
This is indeed an unusual situation. The number of bars indicate signal strength, and the presence of LTE or 4G or 3G or E or even a small circle (GPRS) indicates the stable packet speed.
I myself have seen what you have described: in very bad reception areas, such as in lower level of department stores or basement, the bars would turn to "searching....." or "No Service". At this point there is no voice and data service. But when I relocate to a better reception place, the bars would return, the data indicator (LTE/4G/3G/E/GPRS) would be delayed in appearing, but not by too long......1 or 2 minutes maximum delay.
Have you let it sit idle for longer than, let's say 2 minutes? If we start to toggle airplane mode and disable/enable 3G before the phone has had sufficient time to establish the data speed quality of the current location, that could interfere with the presence of the data speed symbol.
On UMTS systems, the voice is handled by the MSC and the data by the SGSN. Under normal circumstances, when the cell phone can conduct a voice call, the MSC knows where the mobile is, and so should the SGSN.
It seems that your cell phone is having problems re-attaching to the SGSN side after a loss of established radio bearer, and needs to go through a fresh location update in order to attach again.
Please test this scenario out in other locations (same loss of reception and return to reception). If you can duplicate it in other areas, then you should open a trouble ticket with your carrier because may be a real problem with the SGSN side.
This re-attach to SGSN is a basic functionality of any GSM/UMTS phone, and I don't believe iOS7.0.3 made any changes to this portion. The release notes doesn't mention having made changes to functionality in this area. So yes, contact your carrier and open a ticket. They may not do anything for 1 user's report, but they will if more people call in, or if you complain enough about it.
Another test is to use another GSM/UMTS phone, put in your same SIM (with SIM adapter if needed), and see if the same problem can be duplicated.