It's the deep discharge that's a problem for lead acid batteries. If you overspec them greatly so you only discharge them 20% of the way, they'll typically last for years. The datasheet for the particular battery may contain more information about specific usage versus expected life. I know that with a set of SLA batteries that I use at work that if I discharged them 80% of the way each day, they only last 45 days. After doubling the number of batteries, they now last more than nine months between replacements. So by doubling my upfront cost I more than tripled the battery life. I saved money in the long run. Don't think that just because something is called deep discharge that it doesn't hurt the battery.

For the rating of 7.2Ah 20HR, the Ah stands for Ampere-hour, and the 20HR means it is the 20 hour Ah rating. The 7.2Ah means approximately 7.2A for 1 hour or 1A for 7.2 hours. The capacity of a battery depends on the discharge rate(power output). The formula is t = C/I where t is the discharge time in hours, C is the current capacity rating, and I is the current draw. Because you're pulling a relatively high current compared to the battery capacity, it would actually be less because if a battery is discharged at a relatively high rate, the available capacity is lower than you would expected.z