What type are they?  24 , 27 ??

How old are they? 

Have you checked the water level lately?

What are you charging them with?

Your batteries may be the victim of overcharging, if they are charged a week at a time. If the water level is constantly low, this would be a first indication. Many LQs do not have circuitry, that allows the maintenance charging cycles featured in "Float chargers".  If the batteries are left unattended, they can overcharge, their plates will be damaged, and their capacities will be drastically lessened. They can still show a full voltage, but as soon as a load is applied, it will quickly drop off.

A furnace blower can draw several amps, and even with good batteries of a 700 -900 AH rating, it can use much of their capacity in a day or day and a half. Combined with other appliances and lighting, the batteries will be drawn down past the furnace's ignition, operating voltage. Without the blower motor operating, the furnace will then not work.

I would suspect the condition or age of your batteries as being the problem.

Gard

So I am guessing you bought type 27s over the 24s you had? 

Two 24s are sufficient to sustain three days of heat use and all other items in your trailer if in good cared for condition. 

Go to Walmart and buy the digital volt meter that plugs into your 12V outlet this will help you monitor your usage.

I had these guys make me a box last winter to house my propane tanks.  very reasonable and willing to work with my designs.

http://www.hmfinc.com/