power - What happens when an FPGA is powered on and left unconfigured?

I am trying to get a general understanding on what happens if you leave an FPGA unprogrammed for a long duration of time.

Suppose you have an FPGA and you leave it unprogrammed for a long period of time (several minutes to hours after power-on), i.e. no bitstream on it, is this bad for the device? Is it recommended to have some bitstream on a powered-on FPGA at all times? What is the general opinion regarding this?

Are the results different on different devices or manufacturers (Xilinx vs. Altera vs. others)?

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Additional Info:

I have a custom SoC board which uses a Xilinx Virtex-6 FPGA. I also have a Xilinx ML605 which I use for reference purposes.

Custom board: I power-on the board. I notice that I get a short duration of time to program it using XMD (Xilinx Microprocessor Debugger). If I lose the 20-30 sec window, I have to switch off and switch on the board before trying again. This does not happen with an ML605.

When I try to program the custom board over XMD, I get something like:

Error: Device Reset by JPROGRAM command, failed. INIT_COMPLETE did not go high.

Let me know what you think.