What is the longest reasonable distance one may expect to ride on a comfort bike?
I would argue that there is no limitation on distance the biggest limitation you will have will be on: Speed and Comfort over time.
Speed
Comfort bikes arn't made to go fast.  They are designed to be ridden around in a leisurely way.  Variables limiting speed include:

Aerodynamics - you are sitting as upright as possible
% of your speed/strength you can use while pedaling - Mountain bikes are designed so that the rider has good control and can soak up bumps.  Road bikes are designed to be maximally aerodynamic and to allow the rider to use their leg muscles effectively.  Comfort bikes are designed so that you will be comfortable sitting on the seat.  I have always found that when riding a comfort bike I cannot use my muscles nearly as effectively.  On a road or mountain bike it is much easier to use your upper body to provide leverage to your legs out of the saddle.
Weight - shouldn't have an effect on a constant speed but when speeding up you will notice the weight of your bike.  You will also notice the extra weight when climbing.  In all other situation weight shouldn't make any difference.

Comfort over time
Road bikes and to a lesser extent mountain bikes are made to be comfortable for long period of time for more dedicated riders.  Just looking at the seat as a case study we find: wide seats are comfortable immediately but after sitting on it for an extended period of time:

You will experience chaffing
You will possibly need to rock your hips to reach around the seat to push the pedals
You cannot use your entire body properly which may lead to injured muscles
You cannot soak up bumps at all which may lead to a sore/stiff back

Conclusion

If you goal is to cover distance get a new bike.  You will go double your distance.
If your goal is to get a good workout and you are not experiencing discomfort keep your current bike and go further.