Degradation of DNA during RNase A treatment of previously extracted DNA

I wonder if anyone here has had any problems of treating already extracted DNA samples with RNase A, and if you have identified the problem or found a solution. I do know that it is preferred to add the RNase A during extraction, but we have samples (generally extracted with a Phenol-Chloroform protocol) for which there is no original blood/tissue left, and which need to be RNase treated. Thus, we have used Qiagen's RNase A and followed the protocol, which in short is:

Add 1 μl of 10μg/ml RNase A to your sample. Incubate at 37C for 30 minutes.
Add 1/10th volume of 3M NaAc and 2 volumes of ice cold 95% ethanol.
Let rest in freezer for 30 minutes. Spin for 10 minutes at 13.000 rpm.
Remove the ethanol. Add 100 μl ice cold 70% ethanol. Spin for 10
minutes at 13.000 rpm. Remove ethanol. Dry samples in centrifuge.
Resuspend DNA in 1X TE buffer.)

However, for many (most) samples, what was previously DNA of high concentration (and high quality) turns after RNase treatment into very low concentration. I.e. we lose the DNA in the process.

This is not owing to that the original samples would have consisted of mainly RNA; on a gel they would produce a strong band of high molecular weight DNA and little or no smear of shorter fragments.

I'd be grateful for any help on this, since we would want to be able to confidently RNase treat our samples to get rid of RNA, but not risk losing much DNA.