Many times the protagonist (or sometimes the kidnappers) is on the run, he/she is being tracked by the authorities through phone calls in order to be located. Why do they need to have the person being tracked to be on the phone for a minute or two (if I'm not mistaken) to locate him/her? Why not a few seconds? What's the technology behind the phone call tracking? Maybe we should not consider the modern smart phones with GPS on this one.
Typically, no, and maybe yes. No, ending a call in under 1 minute will not prevent a location from being found. Yes, because while the information is known, it takes a while to retrieve (pulling it up from a database, or from the tower, or getting a warrant.)
Land Lines are fixed connections, and figuring out where a call came, what number is dialed, length of the call, is instant. The second you finish dialing, it's logged by the switching system. Telephone switching systems have been digital since ancient history (1970s), and it basically amounts to a pen register or a call to the phone company to find out where it is coming from. In modern times, this can be done via email or dedicated websites for law enforcement. ANI, Automatic Number Identification, is old technology, similar to Caller ID, and will provide the number even for blocked calls. If you have the number, which is immediate, then all it takes is a short amount of time to look up the address.
Cell phones are trickier because you are not fixed to a location. But again, once you know the number, the call can be traced to the tower it is on, and then the cell phone triangulated off multiple surrounding towers. This is easier in urban areas due to the number of towers.
Modern Cell phones are, In the US, by law, required to identify their GPS or Cell-Triangulated location via Enchanced 911. Calls made to 911 from these cell phones should immediately provide the gps coordinates of the cell tower, or the phone (depending on age), directly to the 911 service. Otherwise, this information should require a warrant (or cell server's cooperation), and there may be some delay in getting the information. There generally isn't a requirement for the GPS info for normal calls.
This is all based on routine calls. Calls that are rerouted, transferred, or VOIP will be completely different, depending on how complex the routing is. A call originating in Brooklyn to a VOIP service in Thailand, which is then rerouted through a cell service from Thailand to a Satellite phone in Peru, ad-naseum, to a phone in Manhattan will not be quick or simple to trace.
So to answer the question, unless there is some dialog stating that the call is rerouted, or the person is using some fancy untraceable equipment, the time limit for tracking is nonexistent. Even for a cell phone, they can find where the call came from. They may not get there in time, but once the call is made, the information is there.