According to Bauer-Leander (Historische Grammatik der Hebräischen Sprache des Alten Testaments, 1962), §72y, this is a result of the merger between segol-segol (קֶ֫טֶל) and tsere-segol (קֵ֫טֶל) types:

Da die Type קֶ֫טֶל und קֵ֫טֶל in weitem Umfange lautgesetzlich zusammengefallen sind, kommen natürlich Schwankungen häufig vor. Sehr viele Nomina zeigen im freien Sg. beide Formen, auch schwankt mitunter der Stammvokal vor Suffixen zwischen a, i od. œ: ... קֶ֫צֶף "Zornesausbruch" vor Suff. gew. mit i, aber קֶצְפְּךָ Ps 38:2; ...

My translation:

Since the types קֶ֫טֶל and קֵ֫טֶל have phonetically merged to a large extent, frequent fluctuations are to be expected. Many nouns attest in the free singular both forms, and also the stem vowel for suffices fluctuates from time to time between a, i and œ: ... קֶ֫צֶף "outburst" for suffices usually with i, but קֶצְפְּךָ Ps 38:2; ...

I could not find other literature on this particular form. It seems nobody has a better explanation than this one, which indeed is a little unsatisfying because it explains the form as an exception.

According to Bauer-Leander (Historische Grammatik der Hebräischen Sprache des Alten Testaments, 1922), §72y, this is a result of the merger between segol-segol (קֶ֫טֶל) and tsere-segol (קֵ֫טֶל) types:

Da die Type קֶ֫טֶל und קֵ֫טֶל in weitem Umfange lautgesetzlich zusammengefallen sind, kommen natürlich Schwankungen häufig vor. Sehr viele Nomina zeigen im freien Sg. beide Formen, auch schwankt mitunter der Stammvokal vor Suffixen zwischen a, i od. œ: ... קֶ֫צֶף "Zornesausbruch" vor Suff. gew. mit i, aber קֶצְפְּךָ Ps 38:2; ...

My translation:

Since the types קֶ֫טֶל and קֵ֫טֶל have phonetically merged to a large extent, frequent fluctuations are to be expected. Many nouns attest in the free singular both forms, and also the stem vowel for suffices fluctuates from time to time between a, i and œ: ... קֶ֫צֶף "outburst" for suffices usually with i, but קֶצְפְּךָ Ps 38:2; ...

I could not find other literature on this particular form. It seems nobody has a better explanation than this one, which indeed is a little unsatisfying because it explains the form as an exception.