You can definitely fix this yourself, but I'm not entirely sure from your description which part is "dropping off". It may be a simple fix where something needs to be clipped back into place or you may need to replace something. Please can you take a look at the images below and identify which part you are having trouble with.
Below is the back of the upper spray arm which clips on to the upper rack. It has a grey plastic cover behind which is a large white plastic washer / gasket. The washer simply slots in to the back of the spray arm and the grey cover clips in over the top.
Your description suggests the grey plastic cover and/or the white washer are dropping off. If the grey plastic cover is missing, it may have fallen into the bottom of the washer under the lower rack, in which case you should be able to find it and clip it back on. If it's missing or wont clip back on, you will need to replace the upper spray arm as the cover and washer are not available separately.
This is the water delivery tube which clips to the back wall of the washing compartment. There is a metal clip which secures the tube to the wall. The open hole and one of the spigots slot in to the two holes in the back of the upper spray arm above. The spigot used depends on which height setting the upper rack is on.
Basically, everything simply clips together. If nothing is broken, you should be able to fix this at no cost by simply clipping the offending part back into place.
Hope this helps. If you need further assistance or help locating replacement parts, please let me know what needs to be replaced. Nearly all Bosch parts are available and in stock direct from Bosch.