After I have answered this question many times, I think it would be helpful for SysML users if there is an article to answer such question.
For easy to explain, please see Figure 1. My customers try to use a connector to connect port p1 of SubSystem1 to the port p2 of SubSystem2 but they cannot. So, they have asked me with above question.
BDD is used to define blocks in term of their features and structural relationships with other blocks . Someone may think that the relationships are allowed, so connectors should be allowed too. In fact, the connector is not a relationship. According to UML v2.4.1 Superstructure , the Connector meta-class does not inherit Relationship meta-class or any sub-types of it.
So, how the connector should be used?
If you have read the UML 2.4.1 superstructure , you will see the third constraint of Connector meta-class (from InternalStructures) which say that a connector can only be used to connect between roles which are owned by the classifier that own the connector or the ports of such roles. Even though the SysML specification allow to use connectors across the boundaries of nested properties to connect to properties within them, but connectors still be used within a boundary of a context block.
Thus, connectors should be used within a context classifier, such as SysML Internal Block Diagram (IBD), SysML Parametric Diagram (PAR) and Composite Structure Diagram.
Figure 2 represent an IBD whose context is MainSystem defined in BDD (Figure 1). You can see that the connector can be used to connect between the port p1 of part s1:SubSystem1 and the port p2 of part s2:SubSystem2. In some books, they have explained that the connector should be used in the "usage" concept.
My explanation is, SysML v1.2 Specification  have defined a structure compartment on a block symbol. This compartment can contain any of the graphical elements of an internal block diagram. You may consider that the border of this compartment is equivalent to the frame of IBD whose context is the owner block of the compartment. Thus, connectors can be used in this compartment, even they are in the BDD (Figure 3). However, these connectors still be used to connect roles within the same context block.
I hopefully expect that this article could help you to get a better understanding in using connectors in you model.
 Friedenthal S., Moore A., and Steiner R. "A Practical Guide to SysML: The Systems Modeling Language", 2nd ed. The MK/OMG Press.
 "OMG Unified Modeling Language™ (OMG UML), Superstructure version 2.4.1" [Electronic]
 "OMG Systems Modeling Language (OMG SysML™) version 1.2" [Electronic]
Kritsana Uttamang, PhD.
Analyst Manager / SysML Domain Expert
No Magic Inc.