calmThe battery specification says that its capacity is 12000 mAh (miliampere-hours), which should be 12 Ah (Ampere-hours).
The CPAP's base plate says that when running on 12 VDC, it draws 3 A maximum. If it draws max power all of the time (which I don't think it does), the battery should thus last four hours (3 A * 4 h = 12 Ah). Furthermore, you can't use the full capacity of the battery. Besides the fact that running a Li-Ion battery down to zero can damage it, the voltage on the battery drops so low after it goes below about 20% capacity that the CPAP can't run any longer and shuts itself off. Thus, a run time of 4-6 hours is probably the best that I can expect.
Again, the issue is that none of the larger portable battery sets in Lowe's appeared to have a 12V accessory outlet. They may have had one, but it was not shown on the box or in the picture, and thus the only way I could have found out would have been to open the box, and the boxes weren't the kind that you could open and still be able to reseal them easily. I suppose I could have asked for help, but given the general knowledge of the people I spoke to there, I wasn't very confident in them.
I think I need to clarify something based on one of the comments I've received. I'm heading home on Sunday. (I'm going to see A Spoonful of Sherman tonight at 3Below Theatre, then joining my fellow fans at BASFA's outing to Star Wars Day with the San Jose Giants tomorrow.) Lisa is pretty confident that once the RV is back home where all of the tools are located and where I don't have to use it to both drive around and in which to sleep, she should be able to locate the intermittent fault and repair it. Therefore, there was no point in putting the RV into a shop to try and repair it, as that would have cost me time, a car rental, and hotel rooms. So living with the annoyances and getting somewhat less restful sleep was indicated for the remainder of this trip. I'll live with the 4-6 hours of sleep that I'm actually getting until I head for home on Sunday.