Only in Firefox is the accessible name calculated correctly for a control, with multiple labels.
Even when using Firefox not all screen readers use the accessible name provided by Firefox
Firefox concatenates the 2 labels text without a space so unless you put a space in the second label at the start of the text the last word of the first label and the first word of the send label run together. The accessible name exposed by firefox for the example above is "label textmore label text"
Recommendations
Do not provide multiple labels for a control using the label element. Although it has been possible according as per the HTML/XHTML specifications for many years, this technique is simply not well supported and may never be.
If you have text before and after the input you want to include in the label, wrap the label:
label wrapped example
Example code
<label for="f2">
label text
<input type="text" id="f2">
more label text</label>
Notes: tested and works in JAWS, NVDA and VoiceOver.
If you need more flexibility in control labelling with multiple sources use aria-labelledby:
In IE if you use aria-labelledby with multiple id references or aria-describedby with single or multiple id references, the referenced elements must be what Microsoft terms as accessible HTML elements. The example uses the label element as it makes sense. The example could have used a span (for example) but then tabindex=-1 would have to be added. refer to Making Non accessible Elements Accessible