No, you really should have the timing VI. Otherwise your DAQ will just sample when you ask it to in software. If you really need the 3kS/s, it needs to be hardware timed and set to continuous samples.
What determines your loop rate for when you read the DAQ data? Just thinking you may be trying to get data more often than data is actually coming in. You say you check for data about every 1ms. At a 3kS/s rate, you should have 3 samples available. But that is assuming only 1 channel. The input rate is actually Samples/Channel/Second. So a full scan will be done in 8S/(3kS/s) = 2.7ms. You are trying to read that data too fast. Slow down your loop. Or set the sample rate to 24kS/ch/s.
Or tell the DAQmx Read to get X samples when you try to read the data. As I said before, the default is to just grab all available data (-1). If there is no data, you get no data. But if you specify a set number of points to read at the DAQmx Read, it will wait for that number of samples to come in.