I2C minimum clock speed and reliability
No, there is no minimum frequency, minimum clock frequency is 0, or DC. See the specification, page 48.  

But you will have to pay attention to rise and fall times. Those are 1000 ns and 300 ns maximum, resp. And a longer cable, with some capacitance will influence edges, regardless of frequency.  

It's that capacitance, together with pull-up resistances that will determine rise time. Fall time is not a problem because the FET which pulls the line low has a very low resistance, and then the fall time time constant will be very low as well. So we're left with the rise time. To get a 1000 ns rise time on a 200 pF cable your pull-up resistors shouldn't be larger than 2.2 k&Omega;. (rise time to 90 % of end value.)  



The graph shows maximum pull-up resistance (in &Omega;) versus cable capacitance (in pF) to get 1000 ns rising edges. Note that I2C devices don't have to sink more than 3 mA, therefore at 3.3 V the bus capacitance shouldn't be higher than about 395 pF, otherwise the pull-up resistance would have to be smaller than 1100 &Omega;, and allow more than the 3 mA. That's the greenish dashed lines. For 5 V operation the allowed capacity is even 260 pF, for a 1667 &Omega; pull-up value (the purple dashed lines).