So you are losing the grip even on your 5 rep deadlifts? I would assume you are far below your max on those - so if you are having problems, then your grip is definitely weak.
I have a couple thoughts on this...
1) Nothing helps grip work like fat bars. But like you said, your gym doesn't have any. I think I have heard of guys using towels wrapped around the bar for grip work.
However, here's what I'd do: First, use an alternating grip for deadlifts (which I assume you are doing.) - Make sure to grip the bar first with the hand that is facing up (supinated) and grip it really good. Then grab it with the other hand (pronated). Also, use chalk. Tell the gym to go screw themselves if they don't let you use it. It makes a ton of difference. I couldn't pick up 600+ pounds either with a fairly smooth bar with no chalk.
If you get to the point where you absolutely can't grip the bar without losing it, then go ahead and use straps. If you aren't a competitive powerlifter, then it's better for you to get the back work in.
OK, other ideas that are great:
2) Hex dumbell holds for time. Grab a hex dumbell by the hex end with one hand. Put each finger on a different side of the hex. Make sure no fingers are on the number-etched side. Hold it for time. Start with 30lb dumbells or so. Work up. No need to go much over 40's though.
3) Timed double pronated holds. With a double overhand grip pick up 315 or so and hold it for time. Compete with a partner. Do it for 2-3 sets. Works great for grip strength.
Matt